Larger diameter bullet for worn rifling?

I’ve got an m1 carbine that shoots poorly. I’m talking 5 inch groups at 50ish yards locked in a vice. The rifling is pretty worn down but I don’t want to mess with it enough to get it relined or for a barrel replacement. I don’t shoot it too often but would upping the bullet size to .310-.312 from the standard .308 factory ammo do anything? I’m not an expert on twist rates and speed but I’d figure building up a load with a tighter fit would allow for better accuracy with more surface area engaging the rifling. Thoughts?