Hi Mandy,
You'll see me prominently in that thread you linked. I built and used 5 of those platforms regularly and they worked great. Kids older now so barely used them last season and, after 7 years and storing them outside through Chicago winters, they are in pretty rough shape and I'll likely toss them and start new.... maybe.
They were absolutely awesome though to have around particularly for an above ground with no shallow end.
Those things are very, very buoyant. Even when they filled with water they'd float on the surface partially out of the water so I'm not sure the suction cups of a bath mat will be enough to hold them in place, but give it a shot. You do need to glue something to the bottom to protect your liner, so maybe no downside other than (presumably) higher cost than cabinet shelf liner I used.
I ended up filling bleach bottles with quikrete and it took 2 per platform to hold them down. I would always remind kids to not attempt to swim underneath/ through them because they could get stuck.
Like I said I built and had to make occasional repairs over the years and they were/ are great for family pool parties, so any questions, ask away!
Paul