jfrmeder,
You didn't mention your Savages model, unless it has a match type chamber, neck turning won't really do much good,you could probably "wring out" your best accuracy by finding where ( how long)the bullet likes to be seated, and the correct powder-primer choice, or maybe a better optic.
I have a 12FV, in.223, and a M77VT .308 Ruger and neck turned for both of them, a RCBS case trimmer neck turner, that the cheapest way to go if you have the case trimmer and even bought a Forster hand held . Only thing I got from either was the satisfaction that I had done every thing possible to prep my brass, weight segregation,flash hole deburr, annealing case necks etc.
The Ruger shoots full length resized better than neck size only
the 12FV needed a better stock, not that the original didn't work but the replacment stock fits me better,wasn't the rifle at all.
I'm a gadget guru, picked it up from my old man the more tools I have out at one time to do a certian job the happier I am.
The ops question caused me to look up an article in HANDLOADER Dec. 2008 #275 by Dave Scovill, he states that the best accuracy inhancement he has experienced with most off the shelf rifles, comes from keeping bullet to case run out at a minimum, plus partial full length resizing with a full length die.