We went through quite a bit of infertility testing and procedures when ttc our first son (had shots and induction of ovulation and IUI to get pg) and just started the process again when we got pg with our 2nd (naturally). I would think that if your estrogen is high again that they might treat you other ways before jumping into IVF. I had the same thing happen one cycle. That cycle we went ahead and had the shot to induce ovulation and had an IUI. I didn't even ovulate that month, so I see what they are saying about that (Not ovulating is very rare for me) My numbers did go back to normal the next month.
I had the HSG procedure done twice and while it was a bit uncomfortable, it was really a very simple procedure. Just be sure and take ibuprofin before hand and you should be fine!!
By all means try to get pg after the HSG!!! My doc said that you are the most fertile the 3 months after one b/c it basically cleans you out!! You can start trying the month of the procedure b/c (if I remember right) they do it before you ovulate just to be sure they don't mess up any possible pg. If your dr. doesn't time it this way, please insist that they do.
BTW, I was 34 when I got pg w/#1 and 37 with #2.
Good luck to you, I will keep you in my prayers.