Agree with Alex.
Blockers are most frequently used for transgender teens to delay puberty onset. I don't think that anyone regularly takes HRT with blockers concurrently. I think there may be some overlap initially, but if you're at a proper dose of T there should be no risk of significant E conversion which would render blockers a waste of time/resources.
Is your insurance going to be covering them? AFAIK, blockers are very expensive.