I'm just wondering if sticking something in the goop behind the tile would work, e.g. a little plastic ball, like a BB, on each corner. Or if the backs of those levelers are a suitable thickness, i.e. squish the good to the the thickness of the leveler.
You would never want to leave something hard under the tile, especially under floor tile, as that will be the place the tile will break.
As for maintaining the same depth or height of the tile, that is what a level is for. And, learning how to lay the thinset consistently.
You need to get enough thinset on the substrate first of all. Then you need to get it to stick using the flat side of the trowel. Next, use the correct notch for the tile you have. Large Format, anything over 12x12, requires a 1/2" notch.
Once you get your first tile down, then your level comes into play. I use a torpedo level to check that the first tile is flat in all directions. The tiles you next lay should be at or below the level of the first one. The anti-lippage system will bring them up to the same plane.
As you get further on, use a longer level to get back to square one to make sure that things are on the same plane. You can always add more thinset, or take away some. But, when you lift up on the tile to remove it, make sure you rake the thinset with the notch.
Also, remove the thinset at the edge of the tile before you lay the next. It will help when you go to grout.