Light cast bullet loads may be best for this old barrel.
And, the loads don't have to be all that light.
If your rifle absolutely won't shoot worth a darn with jacketed bullets, cast bullets, properly sized to the bore might be able to restore its accuracy. And with the right bullets, gas checked and cast of the right alloy, velocities up to about 2200fps can be done without leading. And that is .30-30 power.
An old savage that will shoot well enough for deer at .30-30 levels (or slightly less) but not full .300 Savage is better than a wall hanger, any day.
You mention some pits at the muzzle. IF the rifle don't shoot decently with the existing barrel, the first thing to do is have it recrowned, then shoot it some more. Often it wear/damage at the muzzle that makes the difference between "decent" and "worthless".
Being the kind of guy I am, I'd test with jacketed loads (assuming the chamber isn't too bad to cause trouble), then if its too poor, get it recrowned, and try again. IF still poor, then go the cast bullet route. You might just save the expense of a new barrel.
And, if not, then rebarrel it. OR have it bored out for a wildcat round, is another option. IF the chamber is not too badly pitted.