I don't see why they couldn't get Mario Kart ready to go, especially if the architecture is anything like the Wii U.
MK8 was a phenomenal success - both critically, with fans, and in terms of attach rate. There's no reason to mess with it. Take the game engine wholesale, create 16 new tracks, add some characters, and add a proper battle mode to truly differentiate it from its predecessor. Take the Retro tracks as a mix from MK8's new tracks and MK8's old tracks.
Don't call in MK9, just call it Mario Kart NX. MK8 was so good that I really doubt anyone would complain about more of the same on the go.
We're almost talking about an expansion pack as much as a new game. And if developing new tracks and a battle mode genuinely takes that long then just port the original MK8 over as is, and have it ready for launch. Very few games Nintendo makes have that truly mass-market appeal, from kids to students to parents. Even dudebros will sit down for some Mario Kart. It needs to be there at launch, it's infinitely more important than having some mascot platformer. MK8 was such a good game it was utterly wasted on the Wii U. They need to find some kind of way to recycle the work done on it.