For something like 40 years all Savage 110 series rifles were L/A, they didn't even make a S/A. That being said, finding an older Savage 110 at a cheap price is fairly easy and changing out the barrel is a pretty easy job. For a decent gunsmith, it can likely be accomplished in 20 mins including headspacing. I have done just that to an older 110, changing the barrel from the original '06 to .338/06. The entire project cost me under $500., including the original rifle, new E.R. Shaw barrel and a gunsmith installing it and modifying the stock a bit to accommodate the heavier barrel profile.
I own a 673 in .350RM and it's a great caliber (and rifle). There are still some around at bargain prices NIB. I also own a couple .35 Whelens along with the .338/06 already mentioned. The .35 Whelen and .350 RM are pretty much ballistic twins and the fact is that the Whelen will begin to somewhat outperform the .350 with bullet weights 250gr and above. A Savage 110 in '06 would be a simple change to a .35W. Both are excellent calibers, of course, but it's a bit easier to find loads for the .35W (and usually a good bit cheaper too).
I'm not trying to talk you out of your idea, simply mentioning an alternative. The rifle you mention making would be a very good combination, no doubt. Good Luck!