IMHO - I would say that if you don't stablize the floor, then a hard surface product is out. Carpet would stretch as the floor moves. I have seen an orange underlayment that has a small block grid that is supposed to give and is used under tile (can't remember the name of this thing), but from what you said you have an up and down shift as well and I'm not sure this underlayment would work. Someone with experience with this may know better.

How wide is the opening between your kitchen and family room? You might be able to use a t-mold or a reducer between the flooring in each room and run it one direction in the kitchen and opposite direction in the family room and use the wood look vinyl in both. Even if you use another flooring in the family room, you may need a t-mold or reducer between flooring if there is a height difference.

Sorry to hear about the flood. I don't like hexagonal tile installed, either. It looks cool in small samples but not all over the floor, in my opinion. If you're getting cherry wood, you can do all white or all black if you desire. Not sure how a black-and-white patterned tile would look with the cherry, though. It's more your preference as to what you like. ProSource has excellent prices on tile from all the major manufacturers if you're near one. Also, Porcelanosa usually runs a fall sale, the next one being November 27 - December 7, 40% off everything which is high-quality tile and other flooring and wall materials. Since you're gutting the bathroom, you could really go with most anything, including some other color than black or white. The kitchen is separated enough from the bathroom that I don't think you need to feel bound to carry the same theme throughout unless you truly want to.

The best DESIGN option = same tile throughout. The sad thing is the tile may no longer be available. Now you are into some weird design elements that no one explained at the time you installed the wood-look tile. In essence you have "wet" areas that are covered in "wood". You are now looking at having to put traditional looking tile or stone in the living areas normally reserved for wood. This is Bass Akwards in the eyes of many (myself included). Personally, being a cork flooring expert, I would replace carpet with cork floating flooring. It is soft and quiet and is NOT wood looking. But I know cork and I know how to live with its eccentricities. I'm 1% of the population. The other 99% can't handle cork. In an ideal world, you would have used a stone look tile in the kitchen areas and a wood-look tile for the rest of the house because that's traditionally where you would put wood. I would check to see if you can find the original wood-look tile. Be aware you will have issues with colour - assuming you can find the same product. Photos of what you are dealing with could help us.