Con rod damage.

could you be more specific about your rod damage? I've looked at the rod picture and I'm not sure what damage you are referring to. I can't see anything in the shell area. Are you referring to damaged shell surfaces? thanks...

Its the annular groove on the side face of the big end that is the issue.

The wear pattern on the big end shells would be useful to see.
I've seen a few rods with a small amount of scuffing on the big end faces, but nothing as pronounced as this.
It would be useful to understand if the piston little end bosses are allowing the rods to float laterally, or showing signs of scuffing.
As already suggested, a slightly out of kilter rebore or an out of square cylinder deck could be a cause?

Crank end play would not be the issue. It would have to be a huge amount before the end play of the small end plus the end play of the rod were used up. [unless there were a badly designed piston in use]

It could be as simple as the crank grinder left the journal's thrust surface rough.

Or something is a little out of alignment. Bent rods are quite common. [leaky Amal syndrome]

From time to time I get a barrel that can not be bored because the bore is too far out of plumb to make it straight.