Where a lot of folks go wrong is they rarely take into account the amount of non exercise calorie burning they do, aka non exercise activity thermogenesis (NEAT). You see it right here, the sole focus is BMR and exercise alone and very little to NEAT. The problem with this is NEAT can account for almost 30% of the calories you burn that day. 30%! And this can have huge fluctuations day to day. For instance when I work my 12 hour shifts in a hospital along with a workout squeezed in before, my TDEE is roughly 4000. On my off days my calories to maintain is roughly 2800. Im pretty much a sloth besides my workouts and the few errands i have to run. That's a 1200 calories difference. Huge right?? On my off days I consciously have to eat less and usually pull it from carbs and fat sources. Protien is the building block and foundation to your BMR it needs to remain high as possible.
I heard you mentioned TDEE calculators earlier, imo they are complete garbage. Either grossly over or underestimates ones true TDEE. The only way to know your true TDEE is live it and trend the numbers yourself b/c your NEAT can change your TDEE drastically day to day. Some just hire coaches to set up a baseline diet, find your TDEE and adjust from there.
So my point to all this is to make sure your being realistic in your estimated caloric expenditure vs the calories you think you need. You may think you may need cut X out from your diet, or you should try a keto diet or you need to change your cardio/lifting routine but it may be as simple as moving more during the day to burn more/ burn faster. I can assure you one thing your metabolism is not broken.
And as for the T3 it may have a little negative impact for about a month you shouldn't gain any weight if your in a true calorie deficiency. Before you hop on some eca, try some l tyrosine 500mg ane iodine 18mcg empty stomach for a month to give your thyroid a boost naturally.
