Which .308/110 bullet? There were many, many for .30 carbine. Jack O'Connor wrote of the dark, desperate days of WW II when the government was hogging all the bullets and powder and brass (Ghee, do you think) and they loaded, in desperation, .30 Lugar bullets in '06 for varmints. Lousy ballistics and coyotes ran off, but the gun went bang and coyote numbers seemed to drop...
If you over work the bullet, it is going to give lousy performance in any gun. In a .30/30 ... you might need to cut the load or push it up a bit. The .30 FMJ's mil bullets would/should take about anything. In '06 you will possibly apply more force and get worse performance, unless you load way down using, say, the 110 grain .30 short jacket data Hornady has published for that bullet...
You have a bullet. It has a use. Find the performance level it is designed for, work there and you should be happy. Try to haul 10 tons in a pickup and you wouldn't be happy either... Luck.