I wouldn't go over the tile for a couple of reasons. Interior doors may not swing properly, but I'd be real concerned about the slides clearing the new materials. Getting all that tile out will help with overall weight as well.
I took all my kitchen tile out and it was by far the worst, dustiest, miserably single job I've done to this coach. Monaco used some sort of mastic that wasn't designed to come off easily. But if I were to do it over, I still would take it all out. Have you considered hiring a college kid to help you with the demo?
If the tile is in good shape, another option many do is remove the carpet only and butt the new vinyl flooring to the tile. They make nice transition pieces as well.
Bill & Brigitte
06 Windsor PEQ, Cummins 400 ISL
2014 Honda CRV or 2012 Jeep