I looked into cork for my kitchen, and I recall most manufacturers warning against installing cork below grade. We are facing the same issue you are. While I don't like the idea of wall to wall, I'll likely buy carpet tiles, so that if part got wet, it would be much easier/cheaper to replace. Will also make the floor warmer. If you went with cork or wood, you may want to install Dricore subflooring first. That raises the floor about an inch, which isn't too bad.

I have the same set up that you are planning. My kitchenette/wet bar is 15 foot in length . The area in front of it is tiled and the adjacent living area is carpeted. I had a hard time deciding how much to carpet and how much to tile in the lower level. I didn't want to use too much carpet because our floors are heated and I thought the tile floors would be more efficient. The only reason I have carpet in the living area is because our grand kids hang out down there and I thought carpet would be quieter and more comfortable.

Prior to our 07 remodel, we had cork floors in kitchen, DR, entry and adjoining powder room for 18 years. I loved this floor! We didn't treat it with much care and didn't receive care information when the cork floors were installed. So, they received a far amount of water when washed, no added finishes or refinishing. We also have a 22 pound dog who managed to scratch up a lot of woodwork around window areas. The floors held up well. If you'd look close (like eyes a foot away), you could see many scratches from a variety of sources. The excess water caused some seams to curve up a little (only noticeable with bare feet). I really wanted to put in new cork floors, but, got talked out of it by a KD who said colors/patterns weren't right for our new look. We put in porcelain tiles and standing on them hasn't yet been a problem. I probably don't stand on them for more than 90 minutes at a time. If I were to put in cork again, I'd use the floating kind and panels or planks. When replacing the old cork floor, everyone was predicting big problems if we had to deal with glued down panels. The old floor came up easy because no glue. Cork is much more forgiving on uneven subfloors than tile. It took about a days work to even out the subfloor for tile (involved replacing some plywood and a lot of sanding). One of my friends just put in a high end glued down cork tile and they now wish that they had gone with the floating option.

I'm the OP. We just returned from visiting a couple more flooring stores (we've now visited four flooring stores in total). One place today was absolutely excellent as far as having a long-time salesperson/owner who really knows her products and their uses in various applications. In a situation like ours she highly recommends using luxury vinyl sheet with a glue down installation. It will adapt to minor dips in the floor, it is all vinyl so could withstand possible water incursion, it won't have potential dirt in the edges like tiles would if there is a water event in the basement, it is durable (she showed us some great examples of what can be done to it without harming it), and it is reasonably priced (not cheap but not as pricey as many other options we've seen). I liked what I saw in the Mannington line wood-replicas because it is not cheesy looking, and it has an aluminum oxide coating to prevent damage to the floor. This floor would cost about 50% of what a marmoleum floor would cost us. Hope this helps anyone else who is facing the same dilemma we are facing about flooring.