Hurdity has given good feedback. My thoughts would be that if you change things you might be out if the frying pan and into the fire. I certainly wouldn't change to a Conti hrt regime as this would be more progesterone.
I do think as we age our hair changes and will often thin more. A shorter hairstyle might mean less strain on the scalp.
Perhaps discuss a new shorter hairstyle with a good hairdresser that will make the hair look thicker. If you like longer hair, then even a good structured bob that you don't tie up In a ponytail might be better and could frame the face nicely.
It does tend to be more youthful to wear the hair shorter as we age unless one has lustrous thick hair you can arrange into a good style.
My hair is quite fine and I had a long bob style for many years but, like you, I felt my hair was falling out and thinning a lot; I now have my hair as short as possible and with a little hair gel applied to give more volume my hair looks much thicker - it's also much easier to manage but you do need six weekly cuts. DG x