Sir,
I have a 788 remington and have the same problem as your savage. I tried for a long time with 130 grain hollow point Speers and they seemed to be the easiest pointed bullet to get good accuracy with given the limited oal available with the magazine. The bullets were seated deep into the case and the ogive was beneath the case neck, but the bullet was still above the shoulder junction, it looked a little weird, but worked well. I never shot anything other than a coyote with that bullet, but it worked flawlessly on the yote.
I actually bought the 788 for cast bullet shooting and that is what I use if for exclusively now. You might want to look into using a Lyman 311041 or 311291 in your Savage. You should slug the barrel for that too, some of the Savages run on the large size for the bore. I had a slide action Savage 30-30 that I also bought for cast bullet use, but the bore was over sized and when bullets were sized to fit the bore, you couldn't chamber the rounds due to oversized necks. I had the chamber relieved a little with and it worked great, a friend of mine's son now uses that rifle.
Good luck on your adventure.
Graycg