Sorry you are dealing with all this. FYI, we are not supposed to talk self-help on here, just provide general info and share experiences and opinions...
Test prop is not generally used for TRT because it clears out of the body more quickly. But there may be one or two guys who have used it, so maybe they can weigh-in. I have generally heard of it being used in the context of a steroids cycle. It allows the bodybuilder to keep test levels high at the end of a cycle, by starting prop once the cypionate is stopped and has begun to slowly clear from the body. And when prop is stopped, it clears out quickly, which allows the body to recover natural production faster, etc. So that does not help a guy who will be on TRT indefinitely... It just means he will need to inject more frequently.
In terms of labs, getting testosterone, estradiol, SHBG and a complete blood count (including hematocrit) are all pretty standard. As someone who has recently dealt with elevated hematocrit - I dealt with it very effectively by lowering my testosterone, DHT and estradiol levels (stopped HCG and Andractim, plus added low dose anastrazole). For something that is potentially dangerous, I think it is much safer to fix the underlying problem, rather than try to control it with blood donations. I mean, how do you know your hematocrit will stay low until your next blood donation?
Testosterone can also raise blood pressure and cholesterol, so those are also things to keep an eye on.
Again, really sorry you are struggling to get care. Any guy with sub-300 testosterone and symptoms should be taken really seriously. I don't know if it makes a difference in your case, but some doctors consider Clomid to be a more conservative treatment (cheap and easy pill that raises your natural testosterone level). Clomid can cause side effects, but taking a really low dose seems to avoid this for some men.