As far as I know he's eligible, but picking him WOULD break the Internet and I'm not sure he could stands the stress of the job. However there might be some other J6 prisoner who could do the job. I don't know them well enough to choose which one, but a few in GOP caucus might know better. It would make an excellent caucus vote nomination, sure to get media coverage.
For less far out options I with I could go with Rush Limbaugh, but perhaps Bo Snerdly would be the first black Speaker. Steve Bannon would make an interesting threat of a choice. Or some other well documented as conservative, yet less controversial, pundit who's avoided the arena of political service. Bill Whittle comes to mind. IIRC he can't become president because his mom was British, but he's good with media, as his you tube record illustrates.