Are the test models ones that come with the printer, or models you’ve found online? If they’re from online, does the printer ship with any you could try? Something sliced by the manufacturer is most likely to work. If those fail, I’d contact customer support.
I have no experience with resin, but is the resin coin stuck to the screen or the build plate? Are you angling the chess piece or trying to print it straight / vertical? My understanding is that resin prints need to be carefully aligned so they’ll peel of the screen, and big flat surfaces like the bottom of a chess piece won’t.