Don't fret too much! I got my CAS letter in the first week of September and I was in the UK two and a half weeks later, meaning I got my letters from the UK, filed for my loans, got my loan papers, found housing, gave my school my passport copies, booked plane ticket, moved my entire life, said goodbye to family and friends, etc in that amount of time. Even if you get your transcripts and diploma in August, you can fax or email a copy to the university. You should probably bring the official copy of your transcript and diploma when you register at uni, but they don't care about sealed envelopes like US unis do.
I would recommend getting temporary housing and then seeing flats. You can try searching on websites (like gumtree) from the US, like I did, and you can manage to secure accommodations. I spent an entire night looking, emailing, and in the morning, I had one person who was interested. I've been pretty lucky with my housing in the UK, but definitely never perfect. I moved a few times this year, but I'm finally happy in my current flat. There is some issues that need to be dealt with, but if you're lucky enough to have mates like mine, then you'll work through the problems together.
As someone told me, if you're going to do something then do it and finish it. Don't half-ass it and don't waste time regretting it. If you can't get through the paperwork, then how do you expect to survive in the UK? I know telling you not to freak out won't help, but I promise you, once you have that visa in your hand you're gonna think to yourself, "phew, it wasn't that bad."
If your experience in the UK is going to be anything like mine, the visa process will the easy part. I had a lot of ups and downs and a few moments of 'oh, I shouldn't have done this.' Now I love my life (both in the UK and US) and don't regret coming here for a second. I now consider both countries to be home. Sorry if my post is not extremely chipper, but I wanted to say that the process is worth it and completely doable in a short amount of time. Best of luck!