You can put the tiles over the popcorn if you put in furring strips to attach them to. I have trouble making sure the furring strips are even because they are on top of the popcorn. I have redone several rooms but I just spray and scrape off the popcorn. Once the popcorn is off the ceiling is level you can repaint or put up tiles.
Don't know how to install, but sounds like a brilliant idea!
Yep, just have to find a way to keep it level and smooth looking between each panel
Here's an article that should help you with your research for this project. Wishing you the best.