I know this is all theoretical, but I somehow doubt this would have ever happened or even been considered....he hadn't been on the show that long, and had no experience running one (Mirkin was picked because he did). And the fact that he left the show to HOST another says something about what his ambitions really were, I think. A lot of performing comedians make brief stops as writers on other shows as a way of getting themselves going (Demetri Martin for instance did that as a writer for Conan), and then leave to do their own thing. Basically, it's unlikely Conan would have stuck around regardless of which opportunity presented itself for him to actually perform for an audience.
I would have been happy with any of those possibilities really. I loved season 3 and 4 with Jean/Reiss and Martin Kogen/Wolodarsky had formidable Simpsons credits.If ABC or Sony hadn't greenlit The Critic, it's most likely Al Jean and Mike Reiss would have remained showrunners for seasons 5 and 6, which was in the original contract. It's part of the reason they remained consulting producers for 3 years.
If David Mirkin hadn't been brought onboard, the job would have likely gone to Jay Kogen and Wally Wolodarsky. They were the show's senior writers at the time. The reason that didn't pan out is because they were being offered numerous development offers outside the show during the fourth season (Frasier amongst them). Same deal for Jeff Martin, who would eventually run Sabrina the Teenage Witch.