I agree, there is a headspace problem with that ammo. Now, if there is still a headspace problem with factory commercial hunting ammo, then it is a problem that should be addressed.
A .303 groove dia. is a serious difference from the nominal .311" to .315" of most .303's I've known. That is a problem,
but only if the chamber neck will not allow the case neck to expand and release the bullet. In the first case fired, the primer itself shows there is likely enough room provided for this. A simple test is to insert a .303" bullet into a fired case mouth. If it goes in easily, there is sufficient room to safely fire oversized bullets.

Saami suggested headspace is set for maximum headspace at .006", while I think the CIP laws are for a max. of .307".

This rifle's first shot displays much more than that - looking like .025", maybe .030". That is excessive and why the cases are attempting to separate.

The first firing shows the case held "mostly" in the chamber until the pressure dropped. That there is a slight 'ring' shows there was some movement to the rear, thus the amount the primer is protruding is not the full value of the headspace slop.
The second case shows more stretch at the web and thus the re-seated primer is flatter.
The third case shows even more stretch and the unsupported primer could not withstand the pressure against the very end of the firing pin still and thus pierced.