I've flattened two records successfully using the pizza stone method. I didn't put mine in the oven though. I left it in the sun for a few hours (it takes a while to heat the stones). I started in the early morning so that it would heat up gradually and my stones are round, both of those things helped I think. Johnny Winter's album took the longest because it was the most extreme. Duran Duran's record only took a few hours to complete because it wasn't as warped. I sandwiched the records in between silk material. That might be a bad idea. It worked for me though. The records weren't exposed directly to the sun. Just the stones and a little silk took the brunt of it.
So for the tally: I snapped one record (glass sheet, oven); I flattened two records (pizza stone, sun); and the others play as is. This was a fun little experiment!