Hello Mike, I know you don't want to hear this, but if you are going to all the trouble and expense of installing a ceramic tile floor, by all means do it right! Floor elevation problems nearly always pop up, but when I run into a situation like yours, I use my reciprocating saw (Sawzall) and cut under the toe kick(at an angle) to cut out the existing vinyl covered plywood. You have to be careful with the saw and not let it vibrate and bang up the cabinets, but with some care and patience and ear plugs you will be able to cut up against the cabinet. You might have to get out your chisel for some tight spots. After you have torn up all of the vinyl covered plywood, check the subfloor for squeaks. Now is a good time to eliminate those with a few strategically placed drywall screws. Then install your backer board using galvanized roofing nails on about 4" centers. This pain-in-the-rear preparation will pay off for you in the long run. You won't have to come up with some kind of transition strip between the floors of differing elevations, you will have installed the tile over the proper substrate and you'll be able to sneak into the kitchen for a midnight snack like a stealth pilot. Good luck and if you have more questions or comments, I'm all ears!