Ballistics Man, you are between a rock and a hard place. Varmint rifles don't do well at formal BR and BR rifles don't make very good varmint rigs. Your first decision is, What do you want to do? In formal BR, actual competitive NBRSA/IBS/etc., a factory rifle stands little or no chance of being competitive.
That being said, match-winning BR rigs CAN be built on Savage actions. I have one, my nephew has one, and at least one other has been at the IBS matches we hold at our club. Here's the rub -- there not as pretty, not as "Swiss watch" smooth, and compared to custom actions the bolts kinda rattle around. The personality it takes to make a competitive BR shooter usually doesn't like actions with bolts that rattle around when everyone else has a name-brand custom one.
If a Savage action is trued and the bolt lugs are trued for a good square lock-up (like the customs), the action is properly bedded in a modern BR stock, I believe the Savage action will shoot with any other. The key to accuracy is the chamber and the barrel, about all the action has to do is deliver and remove the cartridge and keep the door closed during "ignitiion".
I am fortunate enough to have a full custom BR rifle with BAT action, Jewel trigger, Robertson stock, Krieger barrel, etc., all put together by Jim Borden and it's the most beautiful rifle I've ever seen. The package, including a Leupold 45X Comp scope, cost me $3,800 and it is a work of the best gunsmith art available today. But, if this same rifle was put together by the same craftsman with the same components, to the same quality with a Savage action, it would shoot just as well.
The point is, the same rifle with a Savage action would only save about $500 in the cost and would that be worth it? Not in my mind. With a BAT (or similar) action it is a pride-and-joy ... with a Savage action, shooting just as well as the custom action, it is always something you are explaining or making excuses for.
If what you want is one of the best-shooting varmint rifles in the world that you can take to the range and shoot some impressive BR groups with, then definitely go with the Savage LRPV and shoot the barrel out of it and then put a good new custom barrel on it. It will outshoot even some of the custom rigs and leave you some money to buy some more fun stuff with.
Whatever you decide to do, have fun and burn up some powder ...