1 pointI'd ditch the water filter. Once you get above snowline the only source of water is melting snow, at that point you may as well just boil it. Also the guides will likely take care of that for you. The guides also typically take care of tents/shelters and will likely discourage you from bringing your own tent. In mid to late summer the snowline could be as high as 8000ft (parking lot is at 5400ft) so depending on how comfortable your mountaineering boots are for hiking on trails you might want to consider some lightweight approach shoes. Don't under-estimate how hot and sunny it will get. I'd recommend a sunshirt, sunhat, thin gloves and good sunscreen. Cover up as much skin as possible and apply sunscreen to the rest frequently. A sunhat that you can fit under a helmet (I have an OR sun runner hat) is a huge plus.
1 pointI don't mind sleeping in the shelter, I have always slept well and if you don't have to carry the weight of the tent all the better. Transceiver is not needed in July/August. Don't need a BIG puffy either, a hooded 100 gram Primaloft or similar is the ticket.
1 pointWelcome to CC.com! I'd suggest getting your pack weight down (80 lbs!) and do some steep snow hikes if you have access. RMI should have some other recommendations for your gear (don't bring more than what they list) and training on their website. I was able to climb the DC route with RMI in the year of 2000 so keep that in mind. The RMI bivy shack at Camp Muir is a smelly place that I wouldn't depend on getting a lot of sound sleep the night before summit day. You're in one room with a bunch of other strangers farting and snoring. I think they get you up at midnight anyway so it's not like you're trying to get 8 hours of sleep. On summit day, you'll be teamed up on a rope with people who don't have as much experience/fitness and some folks who have more than you. RMI may turn around folks who aren't comfortable or able to continue at certain points. When I climbed with them (a long time ago) on summit day I switched rope teams 3-4 times as folks dropped off. So long as you have ok weather and you're able to physically keep up, you should be able to continue on to the summit. The DC route in prime climbing season is a circus but interesting enough terrain to keep your attention. Hope that helps -