My rifle has a 26" barrel. I only own a couple of bolt-actions with barrels shorter than 26"...Most are rimfires. I only have 1 centerfire bolt-action 24" barrel...My 5R .308 Win.
If I was going to play with the 06 I would go AI and throat it for the 208-215 grain bullets. Then you can shoot standard 06 brass with great life and still get great long range performance!
Heck that bullet weight range in the standard 06 is pretty impressive.
I would sell the Mossberg and buy one of the 100s of excellent 300 WinMag 700 ADLs out there.
That will do what no improved 06 can do, have some resale value, give you a good basis for a future build and can be loaded down to 30-30 performance should you wish.
I own some strange wildcats, but no rechambered Mossbers.