Keep Kanto mostly the same. Have Ash lose to Gary instead of Richie in the Indigo League, but have Gary lose the round after. Ash continues on to Johto with Brock and Misty going back to their gyms. Ash's new traveling companions are Ethan and Jasmine (more mellow voice to balance out Ethan being more boisterous). Ash acts as a more experienced mentor to Ethan, but still a good way from being a master. Ash still goes after Pokemon, but Ethan is the one who goes after gym badges since Ash already qualifies for the Indigo League. Once Crystal is in development and the anime producers know that Kris exists, have Jasmine return to her gym and introduce Kris, who already has all eight badges but just missed out on the last tournament, so she's traveling around some more until the next one. At the end of the Johto arcs, all three end up in the tournament. Kris defeats Ethan, Ash defeats Kris, and Ash ends up winning the Indigo League, beating Gary in the finals. Ethan is initially devastated, but vows to continue training.
From that point on, the "battle" protagonist of the previous gen acts as a mentor to the new protagonists of the current gens, one of which focuses on battling and the other who focuses on whatever other contest is in the gen, like Pokemon Contests and the Pokeathlon. Ethan goes to Hoenn and travels with Brendan and May, then Brendan goes to Sinnoh and travels with Lucas and Dawn, and so on. Formulaic, but a long-running anime will be formulaic to begin with and at least we get some development in a constantly-evolving world.