You might be able to feed one round of the top with the bullet extending beyond the magazine, but the mag box is too short to hold a loaded 300 RUM cartridge. You need to get a 300 RUM mag box, then open up the mag area of the action to fit it. The easiest way would be to go with the center feed box that sits in the stock so you don't have to mill out the slots to hold the stagger feed box (Does Savage make one?) retaining lips into the action, just open it up and adjust the feed ramp until it cycles which is very easy to do.

Both of my fairly old Savage factory 300 RUM mag boxes were made by Savage out of two 300 Win Mag boxes cut and TIG welded to get the extra length. They have 300 Win stamped on them.

You might also look for a used take off LRH stock with the 338 Lapua bottom metal. That will turn your 300 Win into a 300 RUM fairly cheaply. For the chassis or a take off LRH stock and bottom metal, Accurate Mag makes an extra long 300 RUM magazine which is what I use for mine that feeds perfectly.