I'm sorry your GP is being stubborn about the age you are allowed to have menopause at!
Of course you could be similar to your mum and ten years peri ought to be another clue, but GPs don't have the time to think these days so we end up getting our info here instead.
I just wanted to say I believe my periods stopped due to covid and they didn't start again until over a year later. My family tend to have late babies and late menopause, so I was pleased to be the exception, age 51 when my periods stopped.
After 14 or 15 months of no periods and having hot flashes, I got Evorel Conti which was awful and not worth it so I stopped after a few weeks, but that seemed to reboot my system. My periods started again. In the year and a half since then I've not had more than five weeks between my periods, they are in 3-5 week cycles as they were before covid, longer cycles in winter then shorter in spring, 4 weeks in summer and autumn, same as they were forever before that.
If you aren't absorbing oestrogen well, then why isn't your GP trying you on a higher dose?
It's good your GP does blood tests, most refuse, so at least you know why it's not working. If I were you, I'd try four pumps for a couple of months, fill myself full of extra vitamins just incase that helped absorption and see what happens.
How about warming your skin under hot water to open the pores, then dry and quickly apply the gel? Or use a hairdryer to warm the skin then apply? Your skin can't be that much more impenetrable than anyone else's, but you need to know why it's not getting to your bloodstream. Can it be used vaginally?
I'm nearly 54 now and was told three months ago I'm probably still ovulating. The variation between women is huge. I imagine your GP would tell me I'm post meno with post meno bleeding every month to panic about.