But boxer's question to you is right on the money...any flooring or floorcovering installed over a 'spongy-feeling' subfloor, especially an engineered wood product that is glued, nailed or stapled, is not going to cure the problem one iota. The only wood product that has any chance of stiffening the floor system would be a solid tongue in groove nailed into the joists...and that is my opinion based on my experience.

Ok so it sounds like you have some good, solid professional advice - it’s always nice when you don’t get differing assessments and each pro says the same thing, usually makes it easier. That said, only you can know whether the perpendicular boards would bother you, but I would ask a different question: will it bother you LESS than the existing transitions and height differences? My guess is yes, and I think that once everything is the same level and finish you won’t even notice those boards. We have one that transitions to the tile in the entry from the living room and I never really notice it - and I can be rather type A about those kinds of things lol. I think your freak outs are normal, especially since you are under pressure making a lot of time sensitive decisions while trying to plan a move. Not the best of circumstances for being able to think clearly and not freak out. That said, there are always surprises to be found and things that weren’t noticed in the tours you did before deciding to buy, it’s inevitable once you spend more time in a house that these things pop up - even in GREAT houses. It probably is a great house, and if this is the only “surprise” you discover it truly is a gem and you should feel happy/lucky that it’s very minor and easily fixable. Take a deep breath and hire one of those guys to fix the floors and move on to the 1.3 billion other things on your list to do before you move :-)

It probably makes no difference structurally. It might be easier to use plywood in that it comes in different thicknesses so it would be easier to achieve the correct height of each riser.

@Celadon is right that the gray trend is behind us and has been for several years now. Do I take this right that you will be moving in 10 years? If so, I would keep the tile and save your money for improvements in your permanent retirement home. Also, I am in the middle of a home renovation and can tell you that the work required to prep a slab for wood flooring will be dusty, not to mention the demolition of the existing tile. You could end up with damages to other surfaces taking out that tile, and there will be dust all over everything to clean up. It just doesn't seem worth it when the tile you have now is so nice. If this were old tile or an odd color, then that's a different story, but it looks like you have a light neutral tile that is brand new.