Emmy I think it would be helpful before your next appointment to consider the available options and go with an idea of what you want, and just ask for it.
For example you said you can't take the combined pill because of migraines, but either the desogestrel mini pill or the mirena IUS are still on the table that can get rid of your periods. Estrogen can be used simultaneously with these although you would in theory need an additional progestogen for endometrial protection with the mini pill.
Or you might just want cyclical combined MHT which relieves low estrogen symptoms and aims to regulate bleeding.
They only have 8-10 minutes so asking outright for what you want can really help. Also print off the relevant section of the NICE guidelines regarding perimenopause treatment if they seem uninformed.
As others have said, if all your doctor understands about menopause is hot flushes, then sometimes you just have to meet them where they are at and say you're having them.