What can I do to prevent grout cracking that doesn't raise the tile level?

Question

I'm replacing a 5 ft x 5 ft section of tiles in my kitchen with porcelain tile. The people who originally installed the tile mortared them directly to the plywood subfloor (without any backer board or membrane sheet in between), and that this probably the reason why the grout had been steadily getting worse in the area for the past several years. I cut out a tile to confirm this and found that it was bonded to plywood subfloor with thinset mortar.

Now I'd love to install the new tiles correctly and have them (and the grout between them) last more than a year or two, but apparently all the underlayments that are designed for tile over plywood are, at a minimum, 1/8 inch thick. But, the entire gap between the tile bottom and the plywood subfloor is only ~1/8 inch, which would make the new tile's surface be 1/8 inch (or more) higher than the old tiles. That obviously doesn't work.

I'm not 100% sure on the plywood thickness, but I'd guess 3/4". The floor joists are 2x10s with 16" centers and X-bridging. The outer side is the exterior wall (brick + concrete block) and the inner side is a steel I-beam. The lower story is a finished basement with a suspended ceiling, so I have easy access to the subfloor/joists from below.

What can I do to prevent the new tiles/grout from cracking (due to movement/expansion/contraction in the plywood subfloor) that doesn't raise them above the level of the rest of the tile floor?

Note: I know the "right" answer is probably to redo all of that tile with proper underlayment, but this turns "replacing 30-ish sq ft of tile" into "replacing 300-400 sq feet of tile", which just isn't feasible right now.

EDIT: this is what the subfloor looks like from underneath. Id have to measure, but I think the center of the area where the new tile will go is basically where the ceiling fan is.

Answer 1

Use silicone grout.

If you cannot do anything to stabilize the tiles and are worried the grout will break again, you can use a grout that flexes -> silicone. Most (if not all) manufacturers will carry a silicone version of all their colors, so you can get the exact match.

Given that your existing tiles on rest of the floor did not snap into half yet, the floor seems stable.

Hopefully your floor does not have any joints going across that area, but again, there is really not much space vertically to fix anything.
Your best bet is probably fixing it to look good enough and living with it until you redo whole floor in the far future.

Answer 2

When I had a curbless shower installed, the instructions for the shower pan required that the subfloor under the pan be flush with the top of the floor joists. That is, in order for the pan to be flush with the surrounding subfloor, plywood needed to be cut to fit between the joists and supported with blocking. If I'm not making this clear, you can look at the page 14 of this instruction manual for some images of this configuration (images 19 & 20.)

Since you say you have access to underneath the subfloor, you might be able to bolster and stiffen the existing subfloor in a similar manner. Not with the special hangers shown in that manual, but by cutting plywood to fit snugly between the joists, gluing them to the subfloor from below and securing them with blocking screwed into the joists. Of course, if there are obstructions like cross-bracing, this might be difficult or infeasible.