OP, there is one other option.
You could open up the chamber to an improved 30-06 cartridge. I used to have a reamer that was made up not to cut necks/throats. I needed separate neck/throat reamers to make up the "IMPROVED" chambers and make up reloading dies for those chambers.
The reamer was based on the 30-06 case. It was the same length, but with made initially for a one caliber long, 30 caliber neck. That means the neck of the 06 cartridge would only be .308 long, after the cartridge was fire formed. I had separate neck/throat reamers for 25, 264, 277, 284, 30, 33, 35 caliber bullets.
The sidewall was opened up to a one degree taper and the shoulder was at 40 degrees.
The resulting cartridges had a significant increase in powder capacity over the parent case. Enough to actually make a very noticeable difference in velocities and recoil.
Just about every caliber could safely have the velocities taken within a hundred fps of the Remington and Winchester magnum factory loads.
That was the problem for me. To much recoil.
I finally had the reamer cut down for 308Win cartridges. The last rifle I have left is a 338-08, that was build over 20 years ago. Very nice cartridge, with slightly better performance than the 338 Federal