I keep revisiting this thread, hoping for a Sign. :) Is it ever acceptable to use a shower pan and create a tile threshold over it, thereby making it higher? As for cleaning the nonskid elements of a shower or tub. I have some wonderful nonskid strips in my otherwise very slippery acrylic tub where I take my showers. Yes, they pick up and hold grime a little too well and you can't just go gangbusters cleaning acrylic. The other day I used some Softscrub and a curved nail brush that fits around a couple of fingers. With very little elbow grease ALL the grime was removed and the shape of the nail brush is very ergonomic.

We've seen lots of issues with drains near the door,, just seems like a bad idea. Does your door swing in and out? If so I'd try swinging it in as often as you can instead of our, that way the sweep on the bottom of the door won't push water out.

Typically we match the bathroom floor to the shower floor. If the bathroom floor tile is too large and slippery, we'd cut it into smaller pieces. Do make sure that your shower floor tile is not slippery when wet. There are products that you can put on the tile afterward to add some grit if needed. Your shower most likely has a threshold and make sure that is well-delineated so you won't stub your toes. Keep in mind that natural stone requires more maintenance and is not as resilient as porcelain tile.

What Verbo said. Go down to the subfloor--you already know there are issues with the waterproofing of the existing shower, so putting a new pan in top will just magnify that.