Hi there Brimstone, and welcome.
I also have thyroid problems (autoimmune thyroid disease), and don't convert levothyroxine to t3. From my own research, the opposite of what you've said may be true, that oestrogen can inhibit the body's ability to use thyroid medication, and that thyroid patients on hrt may need increased doses of thyroid medication.
As I understand it, all oestrogen used in hrt is actually bioidentical, and the same as you would be prescribed by a doctor specialising in bioidenticals. It's the progestogen that seems to be different. Most progesterones used in hrt are actually progestogens, which are not the same as our body's own progesterone. The closest to our own (as I understand it, but please do your own research!), is the one in utrogestone. I also suffer from dreadful hot flushes and night sweats without hrt - it's worth remembering though that levothyroxine can cause night sweats - I had dreadful night sweats on levothyroxine long before I was peri - check the side effects on the leaflet.
If you're struggling with thyroid issues, Thyroiduk is a fantastic resource.
I'm sure others who are far more knowledgeable than me will be along soon to help.
Good luck in your journey.