I was told Rimadyl can be harsh on the stomach and is too much for an irratable bowell. At least that is what my vet told me.
Carafate may also be a good choice to try. If there is an ulcerated area in the intestines or stomach that may be slowly healing, this will coat it and help your little guy pass his stuff.
If your guy had problems holding it he could have been so irritated that he couldnt hold it. Now that he has been on a bland diet and his lifestyle is normal, he is improving.
Without doing a biopsy you cant determine that it is IBS< IPSID< or anything else. Prednisone sounds like a maintenance drug to use over time. Carafate will do nothing or help. You could still do the pred and see if it improves anything. Another option is a scope through the throat which can look into the upper intestine.
Pepto bismol in small doses is okay but if given over a long period of time can also become irritating. Great for nausea and lets your pup eat.
Pepsid AC is also great and reduces the acid.
I think that the diet is bland enough that acid shouldnt be a big factor and pepsid and pepto arent really vital until your basenji wont eat or throws up a lot.
Good luck and keep us posted!!