The number one benefit that Ren & Stimpy has over all other franchises is their versatility. Stimpy was always "the stupid one" and Ren was always "the jerk," but everything else about the show was in a constant state of flux. They could be cowboys or vagrants or Hollywood celebrities. So, remember those episodes of Adventure Time with guest directors? Imagine if every episode of the new Ren & Stimpy series was like that. Instead of just a different setting, imagine if every episode had a different art style. Imagine if obscure artists nobody's heard of were each given their own episode. Every time you tune in, you never know what you're going to get. That's the best way to "reinvent" Ren & Stimpy. This doesn't mean John K's influence is going to be left behind entirely, but it allows the show to become so much more than just John K and the things he liked. It can become EVERYTHING.
The only other show like this that I'm aware of is Space Dandy. Each episode had a different creative team, and the only constant was the characters and the setting. It could be a zany sci-fi comedy in one episode to something heartfelt or even melancholy in another. Ren & Stimpy could be the American Space Dandy.
Orrrrr you can just get a bunch of random people who are not John K to try to imitate him. I mean, I love John K's stuff, and I wish there was more stuff like it, but that well is poisoned until the man dies. Once he's dead, we can feel comfortable imitating him, the way people feel comfortable imitating Lovecraft. But until then, let's move Onward and Upwards.
https://www.youtube.com/watch?v=6REAScnP-pU 
