jd168, you are making it much too complicated. If your tiles are not coming off the wall, and if there is no structural damage to the walls or leaks in the floor, and the surfaces are flat, the existing tile is an excellent backing for new tile. You do not need Hardibacker.

Nine years ago, we retiled the shower in our home, built in 1917. The old shower was tiled entirely in glossy porcelain white 4x4 tiles, with a white honeycomb tile floor. We left the existing tile in place and tiled over it. The nine-year-old installation looks like new today.

It is important that the old tile surfaces be scrupulously clean. Years of use will have left soap residues on the surfaces that you want completely off. Wash down with a TSP solution (or TSP substitute), then wash down again. We also took the precaution of having a handyman rough up the surface a bit (he used a router); it is not necessary to rough up every square centimeter, but it helps to have the roughed-up areas not too far separated.

Then lay down a skim coat of latex-amended mortar. (We used Mapei Keraply with Custom thinset.) Mortar is, after all, specifically designed to stick to tile. Cover the entire surface, but keep the coat as thin as you can; you want the surface to be level. Let the thinset dry and cure completely, a couple of days. Then tile just as you would with a Hardibacker surface. Grout with epoxy grout if you want low maintenance grout lines in the wet environment of a shower.

Thank you herring maven for your advice. You make this easier than I thought, although I do not understand how to rough up the surface with a router.
Would an oscillating tool fitted with carbide rasp be able to do the job as well?
Did you use the router to remove the grout from tile joints?
Could I purchase Mapei Keraply with custom thinset at Home Depot?

jd168, I am sure that the oscillating tool fitted with carbide rasp that you describe would do the job. We did not tell the handyman whom we hired how to do the task we assigned him -- to rough up the surface a little -- we just told him the end result that we desired, and the choice of tool was his. Our handyman used a window washer's motion, and we ended up with VERY shallow (less than 1/16" deep, perhaps half that depth) tracks that were 1/2" t 3/4" across and about 2" apart and looked like tiny bicycle tracks.

We left the old grout in place, but, as I wrote earlier, we washed down the wall and floor very thoroughly.

Historically, I think that Lowe's has been a Mapei house and Home Depot carries something else; I am pretty sure that we bought the Mapei Keraply at Lowe's, but we may have bought the Custom thinset at Home Depot.

herring maven: Now I am clear and very appreciative of your assistance. If I ever got this done, I should post a picture