I have no experience with an 06AI, but plenty with a plain jane 06. I am a reloader also, however, I'm not into fireforming brass, so I'd go with the plain jane 06 myself(I did, LOL).
With a 24 inch encore barrel in 30-06, it's not very difficult to handload a 150 grain bullet to 3000 FPS, and I happen to think that the 150 grain bullet is the perfect weight whitetail bullet in an 06.
One of my favorite whitetail rifles is a Remington 760 pump carbine in 06 with an 18 1/2 inch barrel. The beauty of an Encore with a 24 inch 06 barrel is it has the same overall length as my 760 carbine, so you have a compact gun that mounts and swings easily in brush choked tight quarters, yet has a 24 inch barrel to milk maximum velocity from the 06 for the longer shots.
Lastly, the 06 seems to be somewhat looked down upon nowadays as a deer cartridge, everyone seems to want a faster, zippier cartridge and some even think it's absolutely necessary in order to kill a whitetail efficiently. Which is a plus for a buyer looking for an 06 Encore barrel. I bought a 24 inch Encore barrel on the want adds here last year, plain jane 06, sights, blued, new unfired for $170 shipped to my door, pretty hard to beat.
Been killing whitetails with an 06 since the mid sixties, and it works just as well now, as it did then, maybe even a little better with the improvement in bullets, and if the bullet is placed right, the deer will never go much more than 30-40 yards before collapsing, if not a bang flop right on the spot.
Just my personal opinion of course(which my 2 ex wives would say isn't worth the powder to blow it you know where, LMAO).