Winchester builds two length actions, a short and a long. From the long action they make two different configurations, the "regular" long action like you have and the "express" action which is what they use for the .375 H&H, 416 remington, 300 wby, 7mm stw, 300 RUM, etc. The action is physically the same size but they're set up differently. You're trying to turn a regular long action into an express and while it can be done, there's a bit of work involved to do it correctly.
An express action has a longer ejection port so the rear bridge of the action is smaller. This is needed because a full length magnum case like the RUM, .375 H&H, etc. needs the extra opening to fit the rounds. If you look at an express action from the top you'll see the scope mount holes right together instead of the spacing of .860" like on the action you have. The express has a shorter bolt stop which allows the bolt to come farther to the rear along with a shorter ejector. The magazine box is a full 3.600" internal and doesn't have a spacer like the one in your 300 win mag. The Wyatt's box is going to require even more modification.
You can probably make it work without opening the ejection port, it'll just be tight to load rounds. There have been a lot of conversions done without doing the mill work and they seem to work. You'll still need to shorten the bolt stop and ejector or buy the correct ones to replace. The right way to do it though would be to have the ejection port milled to accept the longer round and there are only a few guys I'd let do that on my rifle. One is Mark Penrod in North Manchester, IN. He's a master at M70's and could do it right, it's not something I'd want most other gunsmiths tackling. There are probably a few other things that it'd take to make a M70 feed the 300 RUM round and he'd be the one to do it right. Another that could do it is Dennis Olsen in Plains, MT.
It would be easier to find a M70 already chambered in 300 RUM and start from there. You're going to be in for a lot of work to get it working right from a 300 win mag receiver.