pete in my last house i installed tile on a portion of the floor and carpet on the rest. when I did this - the DITRA product was not available (or at least I had never heard of it). I used a self leveling product and tiled over that - never had a crack and the dogs loved it in the summer (cool bellies!). In the winter - I put down a carpet and the dogs loved it (warm bellies). Tile is a great product for a basement. When I do my next basement project in the new house I will use Ditra first and tile over that. For the rest of my old basement - the carpet was OK but we did have an occasional smell which may have been due to some moisture that would come up around the lolly columns when we had a lot of rain. I think carpet can work OK in the basement but I would put down a raised subfloor first. Take a look at a product called Dricore which provides a rasied subfloor with 1/4 inch air gap. Then carpet over the Dricore. You might also look at some of the new higher end vinyl products. You can get vinyl that looks like hardwood or stone and might work better than the carpet. Again - install over a subfloor with air gap.

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.

As above, you can look at different flooring with the same undertones. If you are working with cool browns, then stay within the same colour family. In lower levels it is nice to work with lighter colours. I take it the cork/PVC is actually a Luxury Vinyl Plank with cork backing? That means the appearance will look like "wood" am I correct? You can minimize the clash by working with a different LOOK (ie. stone or tile looking product rather than wood). If you move away from a wood-look product you will open up a vast amount of potential. It will take a little longer to find a decent compliment, but it will give you the continuity you are looking for without worrying about real wood up against/visible to a faux wood. You can also do yourself a favour by finding the "cork/PVC" product FIRST and then get your sand/refinish done in a complimentary format later. This is probably the easiest way to do it.

https://www.flooranddecor.com/porcelain-tile/truewood-cream-wood-plank-porcelain-tile-100480698.html#srule=Price+Low+to+High2&sz=120&showBrand=true&start=1 There is also this one at about 1/2 the price. https://www.flooranddecor.com/porcelain-tile/bradford-natural-wood-plank-porcelain-tile-100503457.html#srule=Price+Low+to+High2&sz=120&showBrand=true&start=43