You do realise that both periods and withdrawal bleeding on exogenous hormones are entirely optional don't you?
If you feel better with a stable daily dose of estrogen and progesterone, why not just take it continuously, every day? Withdrawal bleeding on menopause hormone therapy or the pill is not medically necessary, it is a relic from a very paternalistic era in women's healthcare when it was believed that women ought to be given an artificial menstrual cycle otherwise they would think they were pregnant.
(Note the dose is usually halved if taken continuously vs cyclical, but doesn't have to be if the 200mg is providing clinical benefit.)
Now if you are still having your own periods, the micronised progesterone is not strong enough to get rid of them, so you would probably continue to bleed. This might be less regular than what you presently have. However you may feel this is worth it if your mental health is better on continuous.
Alternatively you could use a combined oral contraceptive pill taken continuously for menstrual suppression - this is what I use myself and have been bleed free and hormonally stable for many years. I am 45 and have a much better quality of life than others my age who are riding a hormone rollercoaster and bleeding all over the place.
If a combined pill isn't for you, there are also suppressive progestins like desogestrel or slynd that can shut your cycle down and allow you to take transdermal estrogen alongside this.
Some women can even achieve amenorrhoea on a single dose of the mini pill desogestrel which can be taken alongside estrogen and micronised progesterone.
So you have tons of options, and you absolutely do not have to put up with your current situation.