Why the rush? I mean, I know you've listed your reasons why you want to be fast-tracked, but really...why the rush? You've laid out a rather phrenetic post full of angst and anxiety. Yes, we all have emotions tied to our GID, but I think the 2-3 months 'waiting' time might help you and your mom sort out some emotional issues; it may also benefit you to think about the road you are about to embark on. I'm sure it's difficult seeing off your friends in college...however, you post that you delayed college because you couldn't handle it emotionally...you're in a world of emotional turmoil right now - I honestly think waiting a few months for HRT would help your emotions settle down; once you're able to think (without being so emotionally charged), you will have a better chance to lay out solid foundations for your future (TG, work, family, etc).
I know it's difficult - I was (also) faced with the cross-roads of jumping headfirst into HRT (without really thinking about what it do to me physically, emotionally, socially, professionally); I also watched my friends jump one year ahead of me (for post-graduate work) since I was also at an emotionally untenable place (and knew I wouldn't be able to deal with the stress of said post-graduate work). I waited for both, and am happy I did. Looking back, I can't imagine what would have happened had I jumped for the 'magic pill' and started in my early 20s (yes, the physical changes would have been more dramatic...but the emotional and other aspects...for me, they probably would not have gone too well). I suggest you wait the few months; I know some of the emotional angst is being driven by this singular need to begin HRT...but that should only be a 'single' aspect of your life...surely you have other aspects of your life to also focus on in the 2-3 month interim to potentially being HRT. In the meantime...perhaps you can continue to grown in your understanding of HRT, its impact on your body, bloodtests, diet and exercise, etc...heck, I don't know - find a new hobby in your downtime (that's what I did).
Your self-imposed timeline to pass by the time you begin CC - why is it so undesirable to start with androgyny and transition while in CC? Unless you're already so class to passing that a few months of monitored HRT will push you over the edge...I've not met many people whose HRT effects were so drastic that they went from unpassable to passable in a few short months (with the exception that they were already semi-passable or androgynous without HRT...and even then, it wasn't the HRT that made them passable, it was their 'aura' and overall presentation that made them passable). Name change, driver's license...maybe someone else can chime in on those.
And finally (!) - if you do end up scheduling your own appt. with a GP or other physician, please don't walk in their with your letter and demand you receive hormone therapy, or dismiss their medical knowledge if they refuse to prescribe HRT. Maybe prescribing HRT to the TG community just isn't within their scope of comfort, interest, or knowledge base. And honestly - the wait times you list for your TG center are actually not bad (in my experience). My suggestion - just stick it out the few months until you can get into the TG center (plus, they should be more knowledgeable and a better resource for you during the period of your transition).
Just my 2 cents...good luck