Poor baby. Him and you.
I would stick with the advise of the vet who saw him. As long as the tube feeding isn't stressing him out and making him fight you, there is no harm in continuing it for a little while to get him going. Offering only a tablespoon twice a day is not too much by any means. He may need probiotics, he may not. But if you want to add them it certainly can't hurt him. I do recommend the unflavored pedialyte for a few days versus water, just to get him back on track.
The soaks will also help him a lot.
I would wait a minimum of two weeks before I'd offer him a solid prey item. Whole prey is much harder to digest when you have an already stressed and weakened system.
He'll be weak for a while, but if you take it slow he should come around just fine.
Gale