My friend thenomadicartist already submitted a wonderful trip story below, so I'll just give some dry details: 

• The road is paved to the Andrews Creek Trailhead. The remaining 5 miles to 30 Mile Trailhead is gravel / dirt, with minor washboarding, and easily avoidable potholes. We used a Subaru but a passenger car can handle it. 
• Chewuch River Trail: trailhead to 4 Point Lake intersection is in pretty good shape. About 10 minor blowdowns, pretty easy to get around. Three stream crossing, either go across janky logs or use water shoes. We forded the water once; it was up to my knees (5'6") and I used poles. Bugs are pretty bad; I kept reapplying picardin. 
• The next mile after the 4 Point Lake intersection has 12 bad blowdowns with multiple tree jams. We navigated off the trail a bit to negotiate the blowdowns. 
• The Lesamiz Trail is in better shape. Once we got up onto the ridgeline, the bugs were not so bad. There's a steep snow slope within 1/8 mile of Upper Cathedral Lake, maybe 100 yards. I didn't put on my microspikes although I debated it... long way down. There's almost no snow on Cathedral Lake. 
• Cathedral Pass to the Boundary Trail is good shape. Glorious views. 
• Tungsten Trail: 76 downed trees on the trail. As my friend notes, Swamplandia reigns here. You might be good at water-dodging, but your feet will get wet.... there's no avoiding submersion when the entire trail is flooded. Wet boots are your destiny. 
• We stayed at a horse camp a bit past the intersection of the Tungsten and Chewuch River Trails. Nice camp. 

Quick report for 5 days/4 nights and approximately 50 miles on the Cathedral Pass loop. Hope to add some more details later!

The 4th of July weekend seemed like a perfect reason to make the trek out to the Pasayten, which we were hoping was mostly snow-free but still offering alpine goodies.

The road to 30 mile was in great condition for all vehicles, and the pit toilet at the trailhead was stocked and in good shape. NW Forest Pass or America The Beautiful pass was required for parking, and we filled out a self-issued permit at the trailhead.

We headed out on the Chewuch River Trail, the first few miles of which were fairly unassuming - along the river and through the burned forest, but enough to have us huffing with our 40-60 pound pack (some folks packed more avocados than others!).

I believe our first exciting creek crossing came just before the split with the Tungsten trail, where we kept left on the Chewuch and crossed Horseshoe Creek on some lovely bouncy logs.

We kept left at the split to do the loop clockwise, pulling around 12 miles on day one to camp by the turnoff to 4-point Lake. There were a handful of water crossings on this section of trail that kept things interesting, and we managed to cross on logs for most of them but opted to don water shoes and wade through for one ford. Bugs were horrendous at camp, and I was eaten alive!

On day two we dashed our overly ambitious hopes to summit Remmel since we were all tired, and headed straight up to Cathedral Lake instead. The first mile or so leaving the 4-point junction was pretty thick with blowdowns and in some sections we lost the trail for a minute, but they thankfully eased up eventually. It was exciting to finally get alpine views as we emerged from the burn into flowery meadows.

There was one 100-foot or so snow slope on the way to Upper Cathedral that we had to cross, but we all made it fine with boots and poles (we had all packed spikes and axe for this trip but could have done without!). Around 8 miles later, we found a good campsite at Upper Cathedral and enjoyed the blissfully mosquito-free surroundings and the mirrored cliffs of Amphitheater. Temps probably dropped into the low 30s overnight.

The next day we headed back a little bit the way we came in order to head up Amphitheater. We scrambled up the West Peak first, before walking the ridge to tag all the other summits. Views of Cathedral Peak and Lakes were stunning. Amphitheater was a pretty straightforward scramble and well worth it.

We dropped back down to camp for lunch, some of our crazier group members took a dip in the lake, and we headed out in the afternoon to check out Cathedral Peak. We scrambled up the steep slope towards the U-shaped notch in the ridge, enjoying panoramic views en route.

Once on the ridge, some of our group decided to call it a day while the rest of us scrambled a little ways further along the ridge. We didn't make it that far, opting out of a class 3-4 move, and decided to head back down to camp for our 2nd night at the lake, where we were treated to a lovely sunset that painted the cliffsides with alpenglow.

The next morning we bid goodbye to the lake and headed over Cathedral Pass. We oohed and aahed at every changing view of Cathedral Peak, watched some badass rock climbers make their way up, and headed over to the base of Apex Mountain where we dropped packs and hiked up for one last summit of the trip (about a mile each way from the trail). Apex's summit offered more glorious views and good basking spots.

We pressed onwards, aiming to camp at the Tungsten/Chewuch juction (14? 16 miles? for the day). Today's trail specialty was sections of flooded, muddy, unavoidable, squishy watery goodness, and a couple more blowdowns, but we made it back across our bouncy logs and set up at the horse camp for one final night. The bugs were back at it down lower, and I donated more blood to the resident mosquito population.

We boogied the final 8 miles out the next morning to make it to the trailhead before lunch time, for a refreshing dip in the river and some well-earned trailhead beers.

Couple more photos on my instagram if you're interested: https://www.instagram.com/thenomadicartist/

On June 26th we hiked in from Iron Gate trailhead. The parking lot is in good shape and has been expanded to hold about 30 vehicles. It had two when we arrived. We spent the night in the parking lot and then headed up past Sunny Pass and Horseshoe Pass to Louden Lake where we camped for the night. Trail conditions were excellent. We encountered three hikers, 2 rangers on horseback with 2 ponies, and plenty of spring flora. After dinner at Louden, the weather was clear so we hoofed it up to the top of Armstrong to take in the views.

On June 27th, anticipating a couple days of stormy weather, we compressed two days hike into one and pushed all the way to Tungsten Mine. There we staked a claim in the upper cabin, started a fire, collected wood and water, and enjoyed not tenting in the wintry mix (mixed rain and snow). On June 28th we awoke to snow and more wintry mix. We explored the mine and surrounding area. Upon returning to the cabins we met two groups that had arrived. One had 8" of snow dumped on them at Cathedral Pass and the other had hiked the same 14 miles we had, but a day later in much less fun conditions.

On June 29th, we again awoke to clearing skies so we day hiked over to Apex mountain and gained the summit. The views were outstanding with clear skies and good cell phone reception.

On June 30th we awoke to more wintry mix, rain, and rainbows. Since we we were running out of good weather days, we decided to day hike to Ampitheater and if we had time and inclination, climb up Cathedral on the way back. We hiked out to Cathedral Pass and 100 minutes later we were standing on the summit in a cloud. A couple pairs of boots in our group didn't withstand the waterproof tests after crossing a half dozen snow fields. That and damp spirits precluded a summit bid on Cathedral.

On July 1st we packed up and hoofed it down the Tungsten Mine trail to the Basin Creek trail. I counted about 70 down trees in the trail on that section. At the Basic Creek trail, we turned and headed back Northeast, hoping to make a summit bid on Windy Peak the next day. The first couple miles of the trail had been cleared by a trail crew, making it possible for us to reach the "campground" at 5600'. There the trail maintenance ended with enormous jumbles of trees across the trail as far as the eye could see. Having two pack goats in our group, we improved the campground a bit and spent the night before our retreat.

On July 2nd we hiked back down to the Chewuch trail and out to the Chewuch trailhead. From there we walked down the road to Long Swamp. From there, two of us hitch hiked back to the Iron Gate trail road to fetch our trucks and conclude the trip. Upon arrival at the trailhead, we counted 17 vehicles.

Main point of this trip report is to mention that there is a well-defined easy trail leading up from southwest of Amphitheater Mountain all the way to the west peak of the mountain, and from there one can easily stroll off-trail along the ridge over to the north and south peaks.  I haven't seen this trail on any maps and is only briefly mentioned in WTA's description of the Boundary Trail, but I highly recommend if you are in the area and have time for it.

Starting from the Cathedral Driveway Trail, I took the Chewuch River Trail and Lesamiz Trail over to the basin southwest of Amphitheater and set up camp at a tarn. 

On the following day I followed the trail to Upper Cathedral Lake and scrambled up Cathedral Peak.  There is no snow remaining in the summit chasm.  For the second chasm crossing, the standard step-across or jump-across move looked well beyond my risk tolerance.  So I chose to walk across the chockstone just to the right and slightly lower, seeming a much more controlled option (though also exposed).

After Cathedral, I followed the trail over Cathedral Pass and then off-trail up the south ridge of The Pope (peak just northwest of Cathedral).  Some class 3 moves.  Nice view north from the summit.

For Amphitheater, I started at the base southwest of the west peak and headed directly up (class 3), then walked along the gentle ridge to the north peak and to the south peak, and dropped down west-northwest from the south peak (class 2).  Though my ascent and descent were off-trail, as mentioned before there is an established trail to the west peak.  

On the third day, I hiked back out to the Cathedral Driveway Trailhead (AKA Chewuch Trailhead).