Before you punch it out, why don't you pull the barrel and see if a RUM case will fit. I promise you it won't even come close. We have never been able to make full-length (H&H) on Ruger Mark I, Mark II or Hawkeye actions without extensive modifications. A RUM is the length of an H&H and then some.
As far as the belts, they don't hurt a thing- just ignore them. Once you fire a round, you can headspace off the shoulder if that is your preference (what I do).
When you get to these big magnums, they like long barrels to work best. I am only gaining 100 fps between a 7WSM and a 7RUM. The case capacities suggest I should get 300-400 fps more. I just shot 3 different 7mms this morning. I have pushed them all as hard as I dare and the 26" barrel on the big case just isn't enough to really get the best out of it. 26" is the minimum I would ever build one on. The last 2 have been 27- 27 1/2" barrels.
You can get a 300 Winny or 300 WSM to fit but that is about it for the big 30s.
Ruger used to make a Magnum action. They came chambered in such calibers as 416 Rigby and 375 H&H. If you found one of those, you could do it. Ruger came out with their own proprietary 375 cartridge just so it would fit their action.
If you chamber it in 300 RUM, you are going to have a single shot.