Nathanial,
First off welcome to LRH!!
I have not built a rifle chambered in a full length standard belted magnum using an action designed for the RUM rounds at least not with the M70 action.
I have used a Rem 700 action that was originally a 375 RUM to build a 257 STW adn it worked like it was made for it.
I ordered a replacement mag box for the STW size case but found the original RUM box actually feed rounds better. This is probably due to the wider feed lips and the slightly wider RUM mag box allowed the STW case to get under more lip.
Anyway, if you can just take some dummy 300 H&H rounds and see if they will feed well out of the action.
THe very shallow shoulder on the H&H may cause problems with shoulder binding and you may have to get replacement mag box for this round but they are available.
The biggest thing is to see if the feed rails will actually hoid the rounds in the box, especially the second and third as the top rounds are stripped off the top.
Also see that there is not major case body binding as the rounds feed up the mag as well. If there is this may be fixed with the narrower mag box but it may also increase the tendancy for a round to jump past the feed rails when the round above it is cycled.
Just try it with some dummies and see what it does as is, may work fine, may not. I will say if it does not feed properly, it can be hell or impossible to get it to do so. Its easy to take the rails down, pretty hard to add to them.
Try it and let us know what you find.
Like I said, this conversion seems to work pretty well in the M700 action but can not say for sure on the M70.
Good Shooting!!!
Kirby Allen(50)