Jared,
I have to agree with the others comments, with the factory 22" bbl, there isn't much gained. I actually have a .30-06 AI and Mine is a complete custom build.
It's a Remington 700 BDL with a Faijen Laminate stock, Timney trigger and 26" Stainless Kreiger Semi Bull sporter Barrel. I have compared the velocities of a Standard .30-06 from a 22" bbl shooting the same exact load from in my .30-06 AI (it fireformed the case of course) and the 4 " of bbl with the standard .30-06's max load was 200fps just due to the increased bbl length.
Now this doesn't mean that the .30-06 AI isn't a worthwhile cartridge. My rifle shoots a 165g Sierra Gameking at 3200FPS (I chronyed it yesterday), it shoots a 168g Berger VLD at 3124fps (same powder charge). These loads were safely developed using Quick load as a guide.
The Standard .30-06 Shooting a 165g Sierra gameking with a 22" bbl was only getting 2750fps.
So in order to get the velocity, you would need to do both. Now I know you don't want to change the bbl, but I was in the same situation as this action was my father's first hunting rifle. His comment was "boy, that's a really nice rifle, Can I have it back now?!?!?!"
As far a reaming it out, yes it can be done to a .300 Win mag, but the the Bolt face would have to be opened up and a Sako style extractor installed. The bottom would have to be opened up and the feed rails and ramp altered to feed the fatter cartridge. You might consider that the barrel of the rifle, after 40 or so years, may be a little worn as well, so you may be extending the life of the rifle by rebarreling it as well.
Just my thoughts,
Hope this helps,
Dan
Also, I can arrange for a Dummy .30-06 AI round if you would like. Send me a PM if interested.
Dan