I've been using Ambroid "Pro Weld" solvent glue lately and it works
well. It works on Styrene, Butyrate,ABS and Acrylic. You can get it an
any good hobby shop. Test a little corner of the piece you need to
glue. If it deglosses the piece it will probably work.
I've also tack welded stuff like this with a soldering iron but I run
it at a lower temperature with a dimmer.