Make Sonic into a Super Meat Boy game, but with rings, enemies, and power-ups, all in their traditional Sonic roles. Problem solved. Incorporating classic elemental properties (fire, electric, etc) is a cool idea, but I think the main puzzle aspect should focus almost entirely on the timing of jumps, etc. That way you keep the momentum aspect, which I feel is critical in a Sonic game. I don't want to stay in one spot in a level working out what buttons to press or picking the correct element. If I do stay in one area, it better change appearance dramatically over time, with potential consequences, and with no momentum lost fiddling around in shop menus.
You could easily incorporate classic Sonic level design into a Super Meat Boy game, and make it more complex. One of my favourite things about Sonic was the tunnels and the loops. You also had gears and pistons in some levels, etc, and Sonic Spinball was excellent in many ways. Come to think of it, its the pinball aspect of Sonic that should be focused on, minus the bumpers of casino/carnival levels. Those things were hell annoying. Anyway, have tunnels and loops (etc) everywhere, and make them do interesting things.
Story can be simple, but I really like the idea of it being incorporated into an interactive evolving gameplay environment.