Hi your 300AI should be a 300 H&H improved. I would have a gunsmith measure the chamber as you will need dies. Also the barrel twist may not be a 10 it could be 12 as it was commonly used years ago. also check the condition of the bore and especily the throat. if it is a custom chamber that dies are verry expensive you could get it rechambered to 300 Ultramag if it has a barrel with a 10 twist at least 26" long and is not shot out and it is on an action like a Remington that the case is designed around.
The 300 H&H Improved is similar to the 300 Wby in performance.