I would definitely call and complain. Most doctors will go out of their way to ensure that you're able to continue getting prescribed medication on time as needed. If you call, they may find someone who will do it for you ASAP.
I was too late in transitioning for blockers to do anything, but in my experience in being on T and going off for 1 month for surgery, I was fine. No spotting whatsoever. But obviously my residual T levels still would've been higher than yours with just blockers. I would definitely call, I think your concern is legitimate.