I hit the same roadblock at a point. Had every pet I could feasibly get and all leveled. Leveled multiple breeds of strong pets. The only pet I didn't have was the Stunted Direhorn and PvP just wasn't my thing at that time. But I wanted the pet, so I knuckled down and started grinding out the 250 wins.
By the time I was approaching it, it was becoming more and more fun to me. Now, most of the fun of pet battles for me is cooking up new teams for PvP and trying them out. Of course you mentioned that PvP isn't your favorite so that doesn't help you but that's just how it worked out for me.
Best of luck to you and I hope you find some way to continue to enjoy the pet game