OP, I've been where you are, it's absolutely horrendous. I tried absolutely everything in the book, I'm not even stressed any longer, my life is really good, but sleep still elusive, and I know it is directly related to the menopause as my sleep is worse when my other symptoms are, even if I'm on holiday and/or as stress free as I've ever been.
The only, and I really mean only, thing that helps me is amitriptyline. It is an old antidepressant, but not taken as such. It just happen that in addition to helping depressed people, it has also been shown to help with sleep. Unlike sleeping pills, it doesn't help falling asleep but help remaining so for 8h. The recommended dose is much lower than what would be prescribed for depression.
I don't rely on it solely, mainly because its benefits reduces the longer I take it but also because I suffer from some side effects, mainly an upset stomach and uncontrollable hunger. I now take it when I've been through 2 or 3 poor night and desperately need a decent one. The good thing about it is that it is non addictive, and it can be taken as and when needed. Doctors are happy to prescribe (unlike addictive sleeping pills).
Of course it might not work, and some people report horrible dreams taking it. I have found that I dream more, but good dreams. Just like hrt has done miracles sorting some people's sleep, it did nothing for me, and actually made it worse. Anything is worth trying though as poor sleep over time has such a massive effect on life.
By the way, I only get about 40mns deep sleep too, but as long as I get over 1h every 2 or 3 days, I can just about manage. Friday night I had my record, 1h33 mns and the way I felt on Saturday was incredible. It's hard to believe that it's how I use to feel every day, but here we go. My mum was the same and she said that her ability to sleep well came back after the menopause, so there's hope it is not to be like this for the rest of our lives!