Do you have photos of him? Also, since I don’t see it mentioned, how are his teeth?
Sounds like you have 2 (likely related) issues - the rain rot and the weight.
I agree that copper and zinc will likely help the rain rot. I would add an Omega 3 source (my choice is Contribute which is fish oil made by KPP) and potentially some Vit E as well, especially if he mostly eats hay (could be why he gets the rain rot in the winter but not so much in the summer).
I’ve never had success with fat supplements. If he’s not gaining any from it, I’d drop it and put that money towards something else.
Supersport is pretty pricey as an amino acid supplement. Tri Amino and Nutramino are more bang for your buck. Although, you may want to look into something like KIS Trace Low Selenium which has the amino acids, copper + zinc, and vit E covering more bases with one product. AZ Copper Complete and Lone Star Trace from HorseTech are also both good options (you will want to ask for no selenium if adding to a complete feed like Resolve to avoid overdose) with a flaxseed base so could cover the omega 3 as well.
Will your barn offer you a small discount if you provide all his grain? I’ve had barns do that in the past. Will they order in other Tribute products? It may be worthwhile trying a soy free option and see what that does. The KNEZ comes in a soy free option and the Wholesome Senior is soy free. My horse previously did well on the KNEZ but I ultimately took her off of it due to the soy (back then they didn’t have the soy free version).
IIWM, I’d cut the Thyro-L and ultimate finish, get him free choice alfalfa in his stall (could be soak pellets or cubes but ideally hay), switch the supersport to the KIS Low Selenium, add the Contribute and give all that 45 days or so. If he’s not progressing, I’d try the soy free grain probably starting with the Wholesome Blend Senior. My personal feed of choice is Coolstance Copra but it’s not super palatable so I mix it with the Tribute Senior, and I get that’s a PITA not everyone wants to deal with.