5 handi's +.
With a Handi it is best to keep it simple. That is 338-06.
The 338-280AI is fine cartridge if you were using a bolt action. The Handis have a springy action and unless you have a constant .003 headspace you will have trouble fully closing your gun.
Each time you fire a round the case will expand or stretch to fill the chamber and each time you reload the case you need to set the shoulder back the .003 plus whatever stretch you have, maybe one or two thou depending how much your latch can stand or how much it will slide.
So an AI case in that environment does not last any longer than a standard case 8-10 times max. Then you have to make a new batch and fire form again, and fire forming is not just a one shot effort most of the time.
There is absolutely no truth to the less thrust theory in AI cases. Read Nov/04 Precision Shooting Magazine. The article is called "Ackley's Mistake" a very scientific investigation. If you want to save yourself some hassle, expand the necks of the the 06 cases and shoot, no fire forming, just shoot them. Full length size them each time.
I love wildcats and the 338-280AI is a fine one. I am having a 223 rebored and would love to make a 25 wildcat but for the above reason I stay with a standard round the 257 Roberts later if I want I can still make it into a 25-06.
I have a 25-06 Ultra and have learned a lot about the way this rifle operates. One thing for sure it does not like hot loads. But then with so much powder in an 06 case, there is no need for hot loads. The canon balls you hurl out of a 338-06 don't need much extra juice.