Hi Misha -
I just read your previous posts. I hope it's ok to respond from my personal experience, it all sounds so familiar to me...
I really would not worry about taking the Levo 'forever'. When given prescription medicine for a symptom i. e. high cholesterol I am all for trying lifestyle/diet adjustments first. But in this case you are replacing a hormone your body cannot produce in sufficient amounts. The correct replacement dose (which will take a while to establish) will alao quieten down the Hashimoto's.
I remember the Hashi swings. Not knowing what it was I welcomed the sudden weight loss and increased energy and dreaded the slowing down, fattening up and constipation that inevitably followed. This roller coaster plus a huge stress load depleted my adrenals...
Now, at 51, I have decent hair for the first time in my life because my thyroid, diet, supplements, adrenals and digestion are finally at a better (not perfect) level. The hairloss over the decades was soul destroying!
Iron is important and Solgar Gentle Iron is good if constipation is already an issue.
Going gluten free made a huge difference to skin and digestion. Low cortisol is also involved in food sensitivities and digestion problems, it may lead to paradoxal reaction to meds and supplements.
Try to get your ducks in a row before menopause hits. I didn't and feel I am starting over now that all hormones are going haywire.
I hope something in my long reply helps in your quest to get better!