Hello again,
Its been a while since I posted this and I am finally getting this project started. I am taking a new approach this time however.
To recap, I want to retile my kitchen floor. I have a pier and beam house with a deflecto tool rating of L/549. Currently the floor is tiled but laid directly on plywood and old hardwood flooring using some kind of thinset maybe(I bought it this way, even I know better than this

). The current floor is also about 1/4" higher than the abutting hardwood floor. I would like to find a way to do it so the floors are even. I thought the floor should be torn out all the way to the subfloor and just built back up to a height appropriate to make it even. I think its possible because my floor in the bathroom is old tile (probably from when it was built in the 40's) and it is even with the wood and not cracked.
I have had three different people come look at my floor and been given 3 different ways it should be done. One company said I shouldn't do tile because it would crack, they recommended vinyl. One company said it needed all that support and not to tear down to the subfloor. One person did suggest ripping out and building back up but they were not a company specializing in tile floor so I'm a little weary of this.
I am also planning to get new cabinets so tearing out all the floor isn't that big of an incovenience, I just want it done right. I feel like the other companies just don't want to mess with it. So what do ya'll suggest? And if I were to rip it out and build back up, what should I use?
Thank you for all your help!