Re: rem long action to short round
Before you spend much $$ truing your action, tune your trigger, then get a case micrometer like a Wilson or RCBS Precision Mic. Get reading from unfired case before, and read again after. Fire 5 rds for a group and record your before/after measurements.
If your brass is only growing by .001 or .0015; you have good headspace for precision. If more, probably will gain a lot by going to a min oal chamber, IF you are going to handload or will check your factory loads to be sure they are in spec (shorter) with your chamber.
Good trigger, min oal chamber and seating bullets close to or into lands will usually deliver Great Accuracy.
Spend your money FIRST on a great set of rings and quality base, if rifle still isn't delivering 5rd groups around .5" at 100yds look at bedding the stock. Probably don't need to true the action.