Gluing Translucent/Clear Plastic

[Hat Guy]

Hey guys, I'm looking to glue some GW Green Necron Rods and some Ultra Pro Toploader card protectors to some Polyurethane bases and I'd like to avoid fogging and obvious glue lines whilst maintaining strength of the bond. I've tried PVA in the past, but didn't like how it turned out, any suggestions?

[OSHIROmodels]

'Plastic weld' or dichloromethane is probably what your after but I'm not sure what the card protectors are made from 

cheers

James