If you can see daylight between the barrel flats and the action flat, with down pressure by hand as you described, I believe that the fit between the cross bolt and the barrel rib extension needs to be addressed. I have never corrected this situation on a cross bolt gun so would rather not speculate on the best way to do so.

Good luck with the repair. Please let us know how it goes.

SRH

May God bless America and those who defend her.