The cork part of the floor is finished. Wasn't bad to do, about 2 full days I'd guess, although I split it up over a week and a half. Really, any of the laminates are decently easy to install and come out quite well.
We've picked out carpet and will have it installed by a pro. Mostly because we're also doing the stairs and I don't feel like doing them. But also because it just ain't that expensive to have carpet installed. I'm guessing $200 total. Whereas the cork install would have run us more than $1000.

Looking towards the backyard from the wine cellar.
If you look close above, you can imagine the floor sloping from right to left, which it does. Close to 3 inches from the right side of the screen to the left. Which is a problem, because the left side is now 1.5" below the foundation, so I have to figure out how to put floor over the raised foundation wall area. Where the floating slab is 1.5" above the foundation wall, no sweat, I've been using leveling underlayment cement to bring it to uniform height. A few more hundred pounds and I'll have the self-leveling stuff figured out, just in time to re-level the basement bathroom floor.

As the cork meets the stairs and ends in the storage room

our creative ending of the cork where it'll run into carpet. We'll keep the carpet very short and "commercial" so the kids can still play on it, ride skateboards, whatever.