The chamber could be slightly too large, or if using reloads, maybe the shoulder is set back too far. (per the cartridge base tape- testing above - only neck sizing of fired cases in the same gun will alleviate) Short shoulders or sloppy chambers might allow the cartridge enough forward movement or displacement on firing to lessen the firing pin strike force, tho this should not happen only on the first round or two, but elsewhere.
Are the primers fully seated in clean, tight pockets?
But it really sounds like firing pin mechanics - gunk or rough surfaces or a burr somewhere may be sticking things up and weakening or shortening the strike until loosened up by the first few rounds Thickened oil (by evaporation, dirt, or cold) on the fp shaft could do this. I use only dry to touch stuff like Eezox or Corrosion X for that purpose. So good deal on the bolt strip and clean.
I would also check firing pin protrusion and for a shortened/weakened fp spring. (Never, ever, store a firearm cocked - dry firing it on storage will not hurt it, and will help preserve fp spring strength.)
You may find it is a combination of things.
If replacing fp and/or spring, Tubb may make a kit or spring for the Rem? , as well as for the M70 (installed on my 7X57)
You can also buy "overstrength" fp springs. (Wolf?)
Last edited by las; 11/22/20.
