With a 26" bbl you can take advantage of a really big case, and that to me means the .375 RUM. If you really need top performance, then the RUM is the hands-down winner over the AI, which is really no different than the .375 Wby in terms of capacity and performance. Though if you're going to go with a big case, then shooting anything except the biggest bullets (300 grn for the .375 bore) nets you a pretty small advantage.
Note that I shoot a boring old .375 H&H and get 2800-2850 fps from the 260 grn accubond, from a 22" bbl in a very handy rifle. At 2800 that bullet drops 4.0" at 300 yards. If it were going 3000 fps like your proposed load, it would drop 3.5". If you loaded it very hot you might be able to get it going 3200 fps, which brings the drop to 3.0" at the same range... just something to think about before you shell out the cash for RUM brass, and all that extra powder, and cart a 26" bbl around in the brush...