Jack:

each shot blows soot past the rim

I have solved this problem with the RKS cases by:

1.) Reducing pressures by using around 12.5 grains of AA #9, H108 or WC820
2.) Using thick wads to help seal the case mouth until enough pressure builds up to seal the case mouth from brass expansion.
3.) Periodically put a slight bell on the case mouths so they are tight and sealed in the chamber.

I do not peen my case rims. Yes my case rims are also around 0.054" to 0.055" in thickness.

If you wish to shoot higher velocities and pressure then you must bell the case mouths after every shot before reloading.

Dave