Better accuracy @ .22 range? No. Out to 100 yards plus? Yes, HMR will do what no .22lr will. BUT, having read this whole thread, it sounds like a .22 is the best choice for your needs. We all like to talk about tiny groups but there is NO better way to get those than a ton of practice. A "ton" is allot easier to afford with a .22 than it is with the other 2 magnum rimfires, as much as I like them.
So, hands-down, go with the Savage...but try to get your hands on one of those thumbhole stocks before you commit to one. I had a Savage that wore one of those and I liked it on the range (bench shooting) but found it VERY uncomfortable for shooting prone, and impossible on offhand shots. (those, due in part to the gun weight) I'd urge you to consider this gun;
http://www.cabelas.ca/index.cfm?pageID=71§ion=1187&ID=4989
I have the same stock on my 93FV (22 mag) but bought it aftermarket;
