1500 iu HCG per week does not look excessive. However, it may raise estradiol. Get tested regularly for that and ask your doc about anastrozole to help control E2.
But I'm not sure that HCG will help raise your T that much, since HCG is meant to replace low LH. Your LH at 10.2 was already good, and a T of 699 is great, if your bio-available T is also good. Bio-available T is free+weakly bound.
But kudos to your doc for treating your thyroid.
I'd ask your doc if you can just change one thing at a time, to get a better handle on how your body reacts to various treatments. Ask if you can keep on 5gm Androgel (that's a fairly low dose), and skip the HCG for now.
Getting thyroid treated may help your T naturally bounce back. But too long on Androgel will start to suppress your natural production of it.