[lugerholsterrepair]

I would consider rubber cement. It is very forgiving as far as spread/ooze goes. pretty much stays where you put it. A layer on both parts..you can rub it off of places it gets to before you mate them together. It doesn't take much to do the job either! Plus you CAN pry the parts apart..maybe..if you have to separate them. polycarbonate may have to be lightly sanded where the glue is to grip well if it's overly smooth/slick.
Superglue HATES clear plastic..I got some near my dollar store plastic glasses lenses once and just the vapors will cloud it.