" I will be taking my 5 unfired rounds and push them back in and give them another go, and we'll see."
Just a suggestion but if the first two do not fire, save the other three and pull the bullet in one and see if there is powder in the shell. If not, I would send the five shell back to Reminon with a detailed note of the problem. They'll probably send you some fee ammo.
Frankly, I'm not surprised. With the factories ramping up production due to the demand quality control just has to suffer regardless of how closely they check it.
If the offending rounds do fire, then I'd be suspecting the rifle. I'd tear down the bolt and give the insides a good cleaning.
If Remingtom primers are a bit harder and the inside of the bolt a bit dirty, erratic firing pin strikes my also be a part of you accuracy problem with that ammo. Erratic force from the firing pin isn't gonna help one bit regarding accuracy. Winchester primers may have a slightly softer cup, I just don't know but Wichester primers have always seemed to be hotter than most other unless you're using magnum primers.
I'm repeating myself but I believe I'd be cleaning the bolt as one option toward fixing he problem.
Paul B.