When we put porcelain tile in our washroom we had carpet in there. When I hired the tile layers they said the cost of laying tile did not include removing glue down carpet. They merely put fortified thinset and screwed down underlayment (Hardy cement board I think) on that. They put regular thinset on that and set the tiles. I elected to use epoxy grout because my wife was worried about cleaning grout on that floor. That was about 4 years ago and we have had no problems with the install. I'm not sure if fortified thinset would stick to vinyl but a good tile setter should know.

Magg5412 that's lovely! wow. It's been 3 years already since I posted my question and finally went with wood laminate that was less expensive than the luxury vinyl I wanted. We went with Pioneer laminate from Flooring Liquidators (sweetwater) my husband installed himself starting the day we got keys. The 18" tile floor the builder put in kitchen & baths looked so nice that my DH just wouldn't agree to ripping it up for my 'vision' of uninterrupted wood floors. (I just paid a service to steam clean all my ceramic tile where grout got too dirty for me to get it really clean--well worth it!) im in the middle of repainting inside of my house so no good pix. but the 3 years of wear on the laminate only shows where water got spilled near a plant and no one saw. Sweep. Mop. Done.

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.

Go for it. The worst case scenario is you have to lay new plywood. Plywood is normally nailed or screwed down. That is much easier to remove than a thin, nasty top layer of luaun or some other bunk. Of course this could be complicated if the person who put down the plywood was a DIYer who used glue. That makes for one HELL of a nightmare if you have to remove the top layer of plywood and some ding-dong used glue between the layers. I would watch hours and hours and hours of youtube videos. Take extensive lecture notes while watching. Review your notes 3-4 times before you lift a floor scraper/heat gun. Turn off the water to the dishwasher, remove the appliances and then start removing the old vinyl. Give yourself plenty of time. Lots and lots of time. You'll need lots of breaks and a swear jar....but other than that, this should be doable. Remember to find out how to get rid of ALL the excess adhesive. That can often require some heavy scraping and a sander. Any excess adhesive left over will prevent the new product from being glued into place. So you need to remove 97% - 100% of the old glue. You don't have any height to play with so going over it with feathering compound is a no-no in your situation. That means you have to MECHANICALLY remove ALL the adhesive residue. If you find you have more glue than you have time/energy, go ahead and remove the layer of plywood (hopefully there is a layer underneath....there are some really bright bulbs who think a single sheet of underlayment is "good enough") and drop in a new layer. It costs more money...but it can be faster. If you go this route, please do NOT use glue between the sheets! It is killer on the next guy/reno. Just screw it down as per the screw-placement indicators and move on.