I am having a full basement bathroom installed and just wanted to ask a few questions regarding flooring choices.
Half of the basement is already finished. So, we will be breaking through the wall that separates the finished from the unfinished side and adding a bathroom there.

The current finished area is on 2x4 sleepers with 3/4 plywood and covered in carpet.
So the bathroom is framed out with 2x4 sleepers glued and red Tapcon screwed into the cement, with 3/4 tongue and groove underlayment sub-floor.

We were all set to do tile, but I found through a little bit of research that tile over concrete sleepers is a recipe for disaster. Moisture/dampness equals movement of 2x4s and therefore cracked grout/tile.

So, if we decide not to rip up the current floor and do a mudjob, then tile, what are our other options?

Can we do a engineered hardwood on top of 2x4 sleepers?
I'd rather not do vinyl or linoleum...

Any advice is greatly appreciated!