Sorry since i don't have 10 gall i don't know about it. But if you want to try to do what i do. I have 2.5 gall and i do 1-50% and 1-100% water changes a week and like i wrote his tail healing really fast. If you decide to transfer him to 2.5 gall keep 50% of his original water.
Also like you wrote he is eating and there is not changes in his behavior for weeks which is good so hopefully it not fast spreading disease which will kill him fast. So i think watch him very closely make sure his fins don’t get worse, red/black spots don’t get bigger/spread, make sure he don’t get lethargic (lay at the bottom and come up only for air,or may stay at the surface in corner);looks paler,color is dull, turn gray, make sure he don’t have open sores, white cottony patches….
If he getting worse you can use medications since you already treated him with salt and it didn’t help. Just want to be sure that you used right dosage though. What dosage of the aquarium salt did you use?
Good medications for gram negative and gram positive bacteria is Tetracycling API or Maracyn and Maracyn 2. But you need to use both of them together. One is for gram positive and another one for gram negative.
Also I know that Tetracycline API you can mix with Fungas Eliminator by Jungle. So you can treat fish if it has bacterial and fungal infection at once.
Ok I will definitely do that if I decide to move him. He is acting normally, but it seems he is doing a lot of bottom swimming. He's not LAYING on the bottom, but he will "sit" on the bottom, and swim on that level. He still eats and gets excited to see me though. Also his fins look to me like they keep getting worse, but slowly, not rapidly. I'll try to get another picture.