I also have the .177 Kral bullpup and I'm having the same problems as you. If you do manage to adjust the trigger I would be interested to know how as there seems only to be a singe Allen screw which didn't seem to do anything. Regarding accuracy, I have cleaned the barrel several times but to date have only tried JSB Exact 8.44gr doing an average of 787fps with a 6fps spread over 14 shots - no problem with that. Being of a certain age outside temperatures are prohibiting further testing. I have been in contact with Dave Robinson at Range Right who tells me that they have been re-crowning the barrels on some rifles which has helped accuracy although the crown on mine looks OK. However it only needs to be a fraction out of true to cause the shot spread. I too have the single shot tray to try.
I notice we are only 5 miles apart.

Cheers, Phil