Re: base shimming?
Don't bother with a tapered based or shimming. Making the problem more complicated then it needs to be.
Get a set of HIGH (extra high if it will make it under the scope bore distance rules) Burris Sig Zee rings with inserts. Buy a set of inserts (5 , 10 and 20 thou in one box). Put the 20 thou in the rear, 5 thou in the front. Raise the rear of the scope, lower the front. Rezero your scope which will be almost all the way 'down' now.
Go have fun. This is the best and easiest way to shim. Absolutely no stress on the scope tube, don't have to muck about with lapping and all that calculations. Best part is if you change your load and the scope is now shooting too high, swap in less inserts and voila back at it again in 5 minutes.
Oh, you can also rotate the shims to give a variable amount of adjustment. 5 min job at the range. Try doing that with shims - yuck.
With the 270, shooting 500m will need less then 12 min of scope elevation depending on how 'slow' you want to run. That's a big case for silhouette...ouch. You have plenty of scope for the job.
Definitely try the 130gr SST. Way higher BC and superbly accurate. Be careful about stringing. You are using very little powder for that case size and irratic ignition could really screw up your 500m groups.