When I first realized I was transgender (6 months ago) I was glad that at least I didn't have any physical dysphoria. However, like you, these things soon started to bother me. I can stand to pee, but there were a few instances when it REALLY bothered me so I usually pee sitting as well. And with the morning woody it can be bad even sitting.
I don't have any advice for you. In my case I find that I can override the need to sit if I have a good reason to. I just need to warn myself ahead of time. It sounds like that won't work for you though.
And yes, sometimes being in the men's room is a harrowing experience. Usually retreating immediately to a stall helps, but not always.