Ideas to hang five polycarbonate squares to ceiling
Neodymium, Rare earth magnets. 

Very strong, one on each corner will be enough to hold 1.5 lbs.

Use the silicone that you have tested on the panels to attach a magnet to each corner of the panels and let cure for a day. Take the other magnets for the ceiling and turn them so they stick or attract the magnets on the panels and place them on the magnets already adhered to the panels so that they're holding together (one side attracts and one side repels).

Now you can use a clear instant-grip adhesive like loctite  to attach the magnets to the ceiling.

While the ceiling magnets are being held onto the panel magnets, place a little dab of adhesive on each magnet and then place the panel in position on the ceiling. 

You may need to take a long strip of tape and tape the panel up to the ceiling until the adhesive sets.

When it's time to remove them, a putty knife or painters scraper should pop the magnets off.