Thanks for the tip, Nameeri.
Instead of using tape, I have ran two strands of #24 wire on the inside of the frontpanel, one on each side. This way the very edge of the touchscreen lays on the plastic insulation of the wire and there's enough clearance to make the touchscreen work well. The screws can be tightened properly so nothing shakes loose when in use. You can still see the front panel bulge a bit, but at least the touchscreen works well now.
I'll post a couple of pictures of my project later on, so you'll understand why loose parts are not an option
