I have a Savage 11M Hog Hunter in .308 with a medium contour "varmint" style barrel. I believe these are center feed from what I read. Will any savage short action center feed stock with a wide enough barrel channel fit it?

Your Hog Hunter should be the 4.40" spacing...as far as if the barrel channel is wide enough...if it's not take sandpaper and a file til the barrel fits into the barrel channel...it's pretty simple to DIY.

Or order a stock that is ready for a heavy/varmint contour barrel.

I'd go the ordering route...that's what I did with my Model 11 in 6.5 Creedmoor and the varmint barrel:

I got the 223 hog hunter. I got an aluminum bedded stock of ebay from a short action dbm rilfe in max1 camo. Came with the trigger guard, bottom metal, and mag. I pulled the bottom plate off and put it on the internal mag in the hog hunter. I had my local gun smith mill out the spot for the side bolt release following the plastic casting marks. Also he milled the recoil lug to fit the accustock. Did not notice any accuracy change though. Gun shot amazing with either stock but i got a magazine now. Been thinking about doing it with a 308 hog hunter but since my experiences with the 223 i think i would look for a all polymer stock and then i could test which one seems to shoot the best on the 308 and use that one on the 308. My 223 with scope, aluminum stock, bipod, and suppressor im coming in at around 12lbs, that is not very light and would like to save the weight if there is nothing to gain.

Stock and mag details?

Yessir, here you go:

Bell & Carlson Style 4 M40 tan w/black webbing stock
Pacific Tool & Gauge bottom metal w/bottom bolt release
Magpul AICS-style PMAG

Had to do a little inletting around the tang and inside the mag well, but nothing an hour with hand files couldn't accomplish. PT&G wasn't as expensive as other DBM setups and it seems to function just fine. Did require a longer front action screw to be acquired. I ordered a 10 pack of 1/4-28 7/8" stainless ones off eBay for like $6 shipped and it worked. Old one was about 1/8-1/4" too short

Yep, 4.4" spacing center feed on the 11 hog hunter.
The cdi bottom metal just came in today for mine.

Im running that same primary arms scope on my hog hunter. Great scope for the money

It's been ok, I had to go through a couple to get one that didn't have issues with parallax, but PA was very helpful in swapping them out, luckily they're only about 20-30min drive from me.

Pacific Tool & Gauge bottom metal w/bottom bolt release
Magpul AICS-style PMAG

Had to do a little inletting around the tang and inside the mag well, but nothing an hour with hand files couldn't accomplish. PT&G wasn't as expensive as other DBM setups and it seems to function just fine. Did require a longer front action screw to be acquired. I ordered a 10 pack of 1/4-28 7/8" stainless ones off eBay for like $6 shipped and it worked. Old one was about 1/8-1/4" too short

Would this set-up work on a Savage 10T with a lower magazine release? Really like this set-up!!!!

Did you mean bolt release? If so yes - his has the bolt release on the top right side of the trigger guard.

Yep yep, works like a charm. Thanks for the kind words Splinter