Joel didn't really want to leave MST3K, he was just fighting with Jim Mallon and thought it best to leave.
And he didn't do much afterwards, he wrote for America's Funniest Home Videos (along with Josh and Trace and I think Frank), which had to be one of the most sold crushing jobs in existence.
I'm not sure when they first started about reviving it. After MST3K got canceled, Rhino got Mike, Bill, and Kevin to do The Film Crew, 4 DVD releases (and possibly more), however Rhingo apparently decided not to actually release it and sold them to Shout Factory, who released them after some minor dubbing to replace Rhino references.
After that, Mike started Rifftrax. Which seems to have started slowly, but after a few years picked up steam, especially once they started releasing already riffed movies (as opposed to just commentary tracks).
Then Joel started up Cinematic Titanic, which did pretty good in selling out live shows, but didn't seem to get the same traction Rifftrax did with online sales. And presumably they were more expensive and more difficult to coordinate, since they had 6 riffers and were on screen.
Joel killed off CT a couple years ago and then that's when we heard rumors of the MST3K reboot. Several of the CT people seemed to be a bit irked at him closing CT, because they were making money off of it. Mary Jo joined Rifftrax and Trace/Frank started their own riffing venture, The Mads (with poor Josh being left out of anything)
Anyway, I never liked the shorts much, but I did like the Safety Woman one, about the free lance architect who was kidnapped by aliens and given super powers to save children from their own stupidity. Rifftrax did the sequel to the one MST3K did.
(And Shout Factory
started getting into original content last year, their first original release is a horror movie called Fender Bender)
edit: Actually, the first person to try to reboot MST3K was Jim Mallon about 8-9 years ago, had an animated version on his website. It was not well received.