I haven't shot factory ammo in a rifle other than 17 HMR and 22 LR in 35 years. Yes, my Remington throats are so long that a 180 set to .005 off the lands won't stay in the case. I believe they have to be something like .150 off the lands to be fully seated in the case neck. They make quite a jump but that's Remington for you. I've loading the SPS from magazine length 2.815 down to 2.800.
I have a 700 BDL in 30-06 1/10 twist that hase the same L O N G jump. Only likes 150 gr. bullets. It will shoot 1/2 MOA or less with Hornady 150 gr. FMJ and 1/2 MOA with Hornady 150 SPBT. Anything else it shoots MOA or lager. I bought the SPS for fast handling and shooting heavy bullets. It won't shoot heavy bullets and since the 06 shoots 150 gr. I don't need a 308 that only shoots (if it would even shoot) 150 gr. or lighter bullets. After the smith is finishes it won't be as fast handling but will shoot anything from 125 gr. to 180 gr. bullets to 1/4 MOA. That's what the bench-rest rifle he built for me does with me on the trigger and I'm sure the SPS will do the same when he's finished. But it won't be an SPS anymore. It will be a completely custom rifle.
Took me under 100 rounds to work up the loads for the custom gun he built. 1030 rounds and still haven't found anything the SPS will shoot under 2 MOA.
Sounds like your savage has a really short throat. If I remember correctly normal 308 length should be 2.800. Lyman calls for 2.810. My custom rifle is reamed so 2.810 puts the bullet at the lands. I load so the ogive is .005 off the lands. My CZ in .223 likes 53 gr. SMKs .030 of the lands and 65 gr. SGKs .002 off off the lands. It's nice when a chamber is reamed to the proper length. Remingtons cambering leaves a lot to be desired. But I supose if one wants to shoot 220 gr. bullets it's probably right up their ally.