Hi there, Sorry you haven't gotten any responses. I'll tag a few people that might be able to assist you a bit more than I can. My first thoughts are first is there anyway you can get him off of Gravy Train and on to a better quality food? Bulldogs are quite unique and not that the food is causing his constipation but it's full of junk and filler. Try some Libby's canned pumpkin and make sure it's 100% pumpkin not the pie filler. Give him a tablespoon or two twice daily. That should help. Pumpkin will also help with diaherra too. His smell is more than likely due the bad food he's on. You may also want to check his tail pocket (those need to be checked regularily as Bulldog and get gunk in them and develope infections there.) The tail pocket is a divit that's under the tail the base of the spine. Some have small one and some have deep ones and some are hard to check due to how their tail curls.
I've learned so much about dog food since I've been here. Here's a wonder link Dog Food rating. Dog Food Ratings
I'm guessing since he's a rescue (Sally is my rescue girl and was quite finiky when we got her back in May) that he doesn't like the food he's on. Stop with the 2 cups of water and just give him the kibble dry for now. If you have a water dispenser on your fridge, fill his water from that too. Could be he doesn't like the taste of the water? Just tossing that out there for you. Hope this helps a bit, but definately check out a better food. You'll be so happy with the results trust me!!