One thing I have noted in mounting and dismounting my Mega: If I try to take one spring-mounted screw out before loosening the other, it will bind. I loosen one, then the other, alternating until the crossbar is freed. I tighten them the same way: alternating.
While I have never had a screw jam with this cooler, I can see it happening.
I'm an old fart, I like to mess around with mechanical things and I'm no expert, so I have jammed a lot of screws in my time. When I run into a jam, I back off and try to see what is binding the screw. I am very leery of tightening or loosening bound screws. I commend the practice to you.
Does the screw go in easily now that you have freed it? If so, you should be OK. If not, further inspection is in order: are the threads in the mounting bar shot? Are the threads on the screw shot?