This should be considered in my opinion and build off of this. Order your self a custom barrel from Lothar Walther for around $350 in a 1:10 twist 28" to 30" and screw it on your self. The Savage sight has a video guide to show you how to do it. Pretty much chamber a non-fired casing and screw the barrel in until it stops. Tighten the barrel nut and your head spacing is set. To make sure, put two pieces of scotch tape on the head of the casing. Try closing the bolt. If it doesn't close, head spacing is correct, if it does close, repeat step one. You can order a bolt head for 338 Lapua. I know my cousin has a magnum bolt head opened up to fit the Lapua due to ejector position. Sharp shooter supply also has brux and douglas barrels pre cut to fit Savage actions. On a side note, if you want to single feed, the single shot Savage Target action will work just fine. You can eject empty casings, and you will have to pull the bolt to pull a loaded round. Not much of an issue if you are setting in a hide or hill top somewhere.
18538 Magnum Bolt Head,300 WM Box and Follower
Right-bolt, right-port Carbon Steel Long Hinged floorplate Standard AccuTrigger $495.00
Another option would be the Howa Magnum action. This might be big enough of a bolt face with a little help from a smith. Tune the action and trigger and screw on a custom barrel, and you are in a very tight set up.
.375 Ruger HWB23915+ 3+1 in chamber 20 #4 27.75" 5.35 lbs Long .620" 1-12" twist $515.00
Most stock makers have models that will fit these actions. You could build either one of these rifles for under $1500 (no scope, rings, or base).
As far as the 110BA, Rifle Shooter Magazine did a review with a very different opinion of the rifle. They compared it to a 98 BRAVO Barrett (both rifles in 338 Lapua). It was the preffered rifle over the Barrett due to price. There was the complaint about the Mags, but they are AI mags in the Savage. Using different ammo (federal, black hills, Cor-Bon) they both shot sub- MOA to 1000yrds. They said the break was very effective, but very loud abusing anybody standing behind or beside the Savage.
Tank