I have fired three boxes of Rio game loads through my 1954 870. Discovered that every eighth time or so, the gun would fail to lock into battery. Gun is clean, including the notch in the barrel extension that the bolt locks into.

Right away, I suspected something worn inside the old gun, but before making a trip to the 'smith, I fired a box of Remington heavy pheasant loads through it. They fired and cycled through it perfectly (and I have the bruised shoulder to prove it!).

870 experts, what are your thoughts on this?

I've had a similar issue with various guns over the years and it usually boiled down to shell head dimensions versus chamber dimensions.

Measure the unfired rim diameters and case head diameters of the Rio shells and do the same with the Remington shells. Then measure the thickness of the rims on each. My guess (and it's just a guess) is that you might have a minimum dimension chamber and the Rios are of a size that are a hair too large. Not consistently, based upon what you've said, but sporadically.