After reading your post I didn't notice what ranges you intend to hunt are or what range are you confident and/or intend to shoot?? Of all the cartridges that you wrote in your post, to me would be the 300 Winchester magnum if you want to put more punch into the equation. HOWEVER before making any decisions, I strongly suggest that you research (like write down) and compare "just" how much of an increase you are going to get over what you already have, the 30-06 Springfield. If there's a need to "eek" out every single fps/foot pounds of muzzle energy then by all means go with the larger cartridge, however it is important to weigh in the fact that a magnum cartridge does come with a price of recoil, powder and components just to name a few. If you go with a wildcat, then there is the expense of dies as well as the investing of time and money fire forming brass, to name but a few factors.
Presently I put together a Ruger 77 tang safety rifle in 300 Winchester magnum as a Christmas present for my son. He didn't need one, but...he wanted one (we can all appreciate that!!). Last year I bought a rifle that was chambered in 7mm Remington magnum, figuring that it would be a simple rebarrel and "rechamber" from the 7mm RemMag as the bolt face was already a magnum bolt face with a belted case so no issues. Due to COVID prison we were just able to take the rifle out for a break-in the past Sunday; on his birthday 5/9. The rifle definitely is a shooter, but..................there's a feed problem!!! Who knew, I certainly didn't, and presently there's no relief in sight!! Now back to my original, "If you have to "eek" out every single fps/foot pounds of muzzle energy then by all means go with the larger cartridge, however it is important to way in the fact that a magnum cartridge does come with a price". Your/the plan is to open the bolt face and convert what you already have to a magnum cartridge, is there going to be a feed problem (such as mine) are the feed rails going to do what you want them to do, is there going to be an ejection problem or a magazine problem that will have to be addressed?? For me these are factors that have to be added into the equation before doing a build. And.....after all of this an important factor to add into the equation is the cost factor to modify your action to a magnum cartridge to eek out every fps/foot pound of muzzle energy.
Yes it is cool to have a custom chambered, costum built rifle in a different magnum cartridge. I am suggesting take a sensible approach and take the time to research what you intend to build over what you presently have, and to weigh out what the gains are going to be over a rifle that you already have sitting in the safe. The 30-06 is a very versatile cartridge that ought to work quite well on the game that you have stated you want to hunt. Investing in a quality barrel and blueprinting the action "might" be a better option than investing in a conversion to a larger magnum cartridge, on an action that wasn't built for a magnum cartridge. And......after this dissertation I hope this input helps you with your build, and that whatever your decision that the build is a successful one.