Cooper57m: I have several Remington 500 series rimfire Rifles (including two 541-T's!) and NONE of them exhibit this "eccentricity" that you describe.
I am going to pay more attention to your reported phenomenon - as I use them for small game and Varminting almost exclusively and once they are "sighted in" at the range and ammo decided on - they just get used on said game.
Approximately how "high and left" is the first round?
Thanks for any further info.
Hold into the wind
VarmintGuy