I want to finish a 12'x36' part of my basement. The trouble I am having is that it is sloped to a floor drain. I was told that DRIcore and shims would work but the drain is a 2" slope down from the ends and that is way too much to shim. I do have a French drain system going around the exterior walls that drains to this drain so I need to find a way to bring up the floor and not affect the drain. The next trouble is that the floor is painted and I can't seem to remove the paint. Chemicals don't seem to work and a floor grinder didn't either.
I am currently finishing a basement and it almost seems like you are describing mine! Slope, dimensions, and all.
If money is no object then have this section leveled. Easy as that. Will it drain properly. No.
But if you are working on a budget and want it to look nice then you need to look at what options fit. So ceramic flooring is out. Hardwoods, even floating, is out. So either carpet the floor or put down some rubber backed laminate (completely waterproof). We are doing a combo of the waterproof laminate (they sell it in-stock at HD - Lowe's doesn't have it) and carpet in mine. The waterproof laminate comes in like 30 different patterns, looks nice and costs about $3 a sq/f. If your basement has potentially a lot of water issues I would go with the laminate.
Also a note on laminates... Water-resistant is not waterproof. I let the HD stuff sit in a bucket of water and it didn't change for three days. I also got some water-resistant samples (and even some cork-backed "water-proof") samples. All of the others were mushy or expanded a lot after three days. I have to think what would happen if I went on vacation and water got in. Make sure the water-proof stuff is made out of pure "rubber".