Hi Spiderly13, thanks so much for posting with more info. What a difficult situation for you
Your TSH has always been unequivocally within range as you say, yet all but one FT4 are above range & the in range one was also near the top. It's true that some people's results in good health fall naturally outside the ref range, but with those symptoms at perimenopause it's so difficult to be sure what's going on.
Though I also had marked weight loss, taking my weight way too low in peri, this, together with your consistently raised FT4 does make me wonder what's going on. The anxiety, hot flushes & raised heart rate can be due to peri or thyroid dysfunction as I'm sure you know. If your heart rate is consistently raised though, rather than just in short episodes, that would also make me more inclined to think about thyroid as possible cause. I also have Raynaud's btw & had all the other symptoms you mentioned & more throughout peri so I know these don't come without worry at this stage of life when there's a nagging question over possible dodgy thyroid involvement.
Can I ask is your weight too low, or have you just lost a bit? Also do you have any other medical conditions & are you on any supplements or medications, inc HRT?
The normal TSH with raised T4 is unusual & I'm afraid I can't find much research that gives helpful insight. The links are to articles from a Clinical Endocrinology journal & GP Notebook, but the former is complex & I've struggled to make headway with it. The relevant section in the GP Notebook article is headed "normal or raised TSH, raised free thyroid hormones".
I have not copied out extracts, as you may prefer not to read the detail if you are happy with your doctor's guidance.
Clinical Endocrinology
https://onlinelibrary.wiley.com/doi/full/10.1111/j.1365-2265.2011.04023.xGP notebook
https://gpnotebook.com/simplepage.cfm?ID=-1080426419&linkID=63475Can I ask do you know whether you have thyroid antibodies & has anyone tested your FT3?
In your position, if it's some years since you saw an Endocrinologist, I think I'd want further expert advice at this stage, but if your GP doesn't think it necessary & you are happy as you are for now you could watch & wait.
Sorry, this doesn't feel like any help at all but I do feel for you.
Wx