Ah puppies...every time it crosses my mind to get another one right away, I read threads like this.
Disclaimer: I was the proud owner of two, incredibly easy to train bulldogs who had, probably combined 10 accidents in the house. And then I got Truman.
Truman sounds like a lot like Baxter, including in the rolling in his own ***** part.
I agree with what the others have said - no more potty side of the pet apartment. It might work for some dogs, it's not working for Baxter. And honestly, this isn't a breed that is eager to please or terribly bothered by dirt and muck so I think many of the training techniques and ideas for other dogs just don't apply.
A few suggestions: make the sleep side of Baxter's crate an absolute haven for him, and the way to a bulldog's heart, is through the belly. Feed him in his crate. Give him treats in his crate. Give him affection in his crate. But when it's time for bed - no potty area, no pads, no towels - just him. Trust me, he'll be just fine and without the absorbent materials, he'll be less inclined to pee or poo. Plus, he'll start to associate crate with eating and goodies and attention - all things he wants.
As for the going out in the condo situation, it's hard but we know the puppy pads aren't really working so I would definitely try that patch of grass to see if you can get him to associate potty with something that at least looks like outside.
I know how frustrating it is to try to train a dog who seems to defy every single thing pet trainers tell you dogs WILL NOT do - but with positive reinforcement, less opportunity, and consistency, Baxter will get it.