There is a fairly easy way to check head space using a case of known length, strips of scotch tape and an accurate measuring tool. If it is much longer than 1.300, it very well might not fire case lengths as short as 1.280. I have known some people to install a longer firing pin and keep shooting.
I’d still be looking for some ammo with longer brass, I just don’t like shooting stuff that short. Of course, you may have some other issue, but you have to ascertain the condition of the action to start ruling-out possible problems. Usually, the extractor will hold the case close enough to the bolt face to fire, but the only explanation for the failure to fire when the muzzle is pointed down, seems to be the case falling deeper into the chamber away from the bolt-face.
Have you checked firing pin protrusion?