Hi Tanuki and a big hug and welcome

I'm sure there will be others along soon more versed in HRT than me but I just wanted you to know that you're not going mad. I had the same peri menopausal symptoms as you and struggled on alone for quite some time before being offered anti depressants which initially I didn't take. Then I went down the herbal route with limited success. You've done the right thing by going to your GP and it was good to hear that they didn't automatically offer you anti depressants.
I think they tend to start off by prescribing Elleste Duet and no doubt, it works for many women. However, it can be trial and error to find one that suits and if you have an intolerance to the type of progesterone in them, you may need to change to a kinder progesterone e.g. femeston. You can print off the HRT types from the website and take it to your doc to discuss but apart from cost, I see no reason why you can't take separate oestrogen as a patch or gel and progesterone orally or vaginally if the Elleste doesn't work for you. BUT you need to start somewhere and apparently you need to try them for a few months to see how things settle. I'm just about to start on my 4th HRT regime and am a bit anxious as I'm wary of the side effects of the progesterone based on my experience to date.
Keep a diary- the sequential Elleste didn't give me headaches but when they switched to cyclical HRT, boy did I have headaches, ditto with cyclical patches. my moods did get worse ( like PMT ) when I was on the progesterone part of Elleste but you'll only know for sure if you keep a diary. As you're peri you'll be only offered sequential HRT so only take it for part of the month. Try your GP again and let us know how you get on. Hopefully your sweats and insomnia should get better soon x