Dave,
On paper, the 7mm, 300, and 375 RUM all have the exact same headspace measurement. Meaning the only difference dimensionally between the three is the neck diameter and the resulting neck length.
That said, what is printed on paper and what makes it out the door from Rem are at times two different things unfortunately.
I recently encountered a batch of 7mm RUM cases that were roughly 0.010" shorter from the rim to the shoulder/neck junction then any others I have used in the 270 Allen Mag.
As there is only a 0.007" deduction in the 7mm RUMs neck diameter to that of the 270-7mm RUM(fireforming load), this is not enough to produce a positive shoulder to gas seal off from. Even if you only size the first 2/3 of the case neck this is not enough to limit case stretching.
The problem is that I generally use match grade striker assemblies in my Allen Magnums and with the heavier striker spring, when the striker impacts the primer, it will drive the case forward in the chamber until it is physically stopped by the case shoulder. Normally, the 0.004" crush fit built into these chambers totally eliminates this problem but when the parent case has its shoulder set back 0.010" farther to start with you can not control this.
The resulting fireformed brass will have a slight thinning just ahead of the case head, the start of case head seperation.
Now if you only neck size or partial FL size this is not a real concern but it is an issue that is easily corrected by using 300 RUM brass instead of the 7mm RUM at least this was my thinking so I tested it out.
Everything seemed to work fine, even case neck thickness was not a problem, in fact it tightened the chamber to neck fit up by a couple ten thou while still allowing enough room for safe bullet release on firing.
Best of all, no matter where the factory shoulder is located, using 300 RUM brass, when you neck the case down to 270 you can position that neck where ever you want to offer a positive gas seal which will eliminate case head stretching.
I do recommend that you make sure the neck diameter is such that will work safely in the rifle though before heading to full tilt loads.
The 300 RUM from federal should work fine in your 7mm RUM. Just check for case length after sizing and neck diameters as well. You may need to turn your necks slightly but I doubt it. Still, check before you start shooting.
Kirby Allen(50)