It's a shame you don't reload. That cuts a ton of options out. There is new life being breathed into the 30-06 every day. Long range bullets designed to run in the 1-10" twists. Whenever I hear people going to a magnum to shoot short action ranges I think that most people don't understand, it's about bullet efficiency not out and out power.
Have you considered buying custom ammo in bulk? It's not a lot more expensive than off the shelf, but you get what you want. As noted in my previous paragraph Flatlines are tearing up the courses everywhere. Simply a phenomenal bullet. Nosler with their long range accubonds, Sierra with their new tipped, Hornady with their new ELD-X/M lineups, will make your 30-06 reach where it never could before. There is no need to go to a magnum unless you want to stretch past 2k. There is very little on the shelf that will compete with the right bullet/case combo. Even the good stuff out there is on the anemic side as they have to match up to a number of different rifles. Custom ammo is tuned to your rifle.
We had this discussion recently in a post called 2000 yd. SA cartridge. What many don't understand is a SA will get there with the right bullets. The alternative seemed to be one magnum or other. This also applies to standard long action cartridges. Cartridges based on the Mauser, .284 and 30-06 cases. These long action cartridges extend the range past what a SA cartridge can do. Without the issues that a magnum will cause you.
Try the custom ammo route first. If it isn't to your liking, you might discuss with the loader a better barrel option. If you don't see it going anywhere, then think about a new rifle. I'd hang on to what you've got though. A new barrel in that stock in any -06 case would be mint. You might even see about setting it up for a DBM. McMillan can do that. So can a number of others.
