I know I'm late to the party, but I wanted to add my thoughts.
The most important thing, Walderness, is that medicine is a conservative profession. People have a vested interest in protecting the status quo. But just because something has always been one way doesn't mean it can't, and shouldn't, change.
Not to be trite but thirty years ago women were discouraged from entering medicine. Everyone "knew" that q2 call was required, that there was no possibility for time off for pregnancy and maternity leave, and that women lacked the stamina and capacity to put themselves through the rigors of training-- especially surgical training. Now of course this is all thrown out the window like the rubbish it is.
The biggest force to reckon with in enacting that change was answering the question "why? Why should women become doctors? Why should we make these accommodations?" Putting aside questions of equality for a second, the main reason is that women brought something to the table as doctors that men didn't. And those things, tangible and intangible, were very valuable. The same would absolutely be true of you-- just like this Jesse mentor you've mentioned, your ability to connect with patients with disability would be outstanding. Your very existence would give them hope. You would be marvelously effective.
And it is because of that added utility that it's worth it to make accommodations for you. I'm not saying you should approach this at all from a "rights" perspective, but there is a reason for which it makes sense for the system to bend its rules.
So what everyone is emphasizing to you is that the current system makes it quite difficult to successfully complete the clinical years and internship of medical training. Fine. Get an assistant to help write in the charts (pay them yourself if you have to). Take the elevators on rounds. Get in earlier than everyone else and stay later to make sure your share of the work is done.
Frankly yes-- the current requirements of training state that we students are supposed to have seen a certain number of procedures and be competent at the physical exam to graduate. You don't have to perform anything to graduate-- not even drawing blood-- let alone insert lines and run a code. And the vast majority of physicians never do anything outside of their specialty ever again after med school... if you never personally deliver a baby with your own hands, you'll be all right. This is anathema to the medical establishment but honestly, you will.
Interestingly, the negative responders to your post who are upper-year med students and residents are all in procedure-rich fields like EM, Ob/gyn and surgery. They most likely find it difficult to conceive of practicing medicine without your hands. But I assure you many docs do just that.
And lastly, not to discourage you, but there are some astounding alternative paths you could take. I would think a PhD in clinical neuropsych, and a subsequent practice entirely of patients with physical disabilities, would be a wonderful way to use your smarts and your experience.
Best of luck to you.
, at the naysayers. 
