I too have the 10" BAT and Stiller Python, Nesika but for the money on a custom "varmint" rig, I think the Predator is the go to action. You have a custom 700 size action that is twice as tight as a tuned 700, cheaper considering the blueprinting costs and slightly more loose (.003) than a full blown BR action. You can go singleshot or magazine depending on how your order it and all for same price.
Now if money is no object, then BAT is top of the list in my opinion. However, for varmint rig that is custom, tighter and smoother than a tuned 700 but not as tight as a full blown BR gun, then the Predator fits the bill and saves $300-500.
For varmint caliber, go to Richards microfit website link at at www.6mmbr.com
and read about his favorite LR varmint caliber the 6mm Ack imp. Not a barrel burner and super ballistics and great accuracy. The 22-243 is a barrel burner supreme. Might consider the 22 BR instead.
I will say that my Stiller Python is just as smooth and fast as my BAT and cost $400 less.