Hello, I'm sorry to hear about Casey and I'd like to help.
I don't think the urinary tract infection and the symptoms that you are seeing now are related.
It sounds like he is a fellow that likes to find things and eat them as evidenced by the rabbit fur hat episode and potato bits that you were unaware he had even gotten into. That can lead to gastrointestinal irritation; even if he is able to pass the foreign material it can still cause upset and mechanical irritation to the intestinal tract.
I think at this point a veterinary visit is a great idea to make sure that he hasn't eaten something that could cause a partial obstruction. We know he doesn't have a full obstruction as he continues to pass stool and eat without vomiting.
In the meantime to try and settle his stomach you can try either:
1) Pepcid-ac (famotidine) at one 10mg tablet per 20 to 40 pounds of body weight
every 12 hours.
2) Prilosec (omeprazole) at one 10mg tablet per 20 to 40 pounds of body weight
every 24 hours.
These will reduce stomach acid and should help if this is related to simple nausea and gastrointestinal irritation.
You may also want to feed a bland diet. It appears that you have been trying something like that but I recommend a bland diet consisting of 1/3 boiled hamburger (or white skinless chicken), all fats and juices drained off, mixed with 2/3 boiled, plain white rice. Feed several small meals a day. You might wish to add 1 to 2 tablespoon(s) of canned pumpkin to each meal if you feel there may still be pieces of rabbit fur or other foreign material to push through the gastrointestinal tract and because you have seen mucous in his stool (the slimy material) as fiber helps soothe an irritated colon.
When you have him seen by his veterinarian I also recommend that some blood tests be run to make sure that his internal organs are functioning normally. It is rare to see a urinary tract infection in a young, healthy male dog and we do want to make sure that there isn't any underlying problems that need to be addressed.
Best of luck with your fellow, please let me know if you have any further questions.