Performance obviously goes to the 7mmLRM - there's no replacement for displacement.
If 7mm performance is your primary criteria, the decision is already made the 7mm LRH is the obvious winner in this.
If off-the-shelf ammo in case of some epic fail, then 7mm RM is the "safer" avenue. Even 7mm RM brass is usually more readily available if reloading. I also struggle with this as I plan a re-build - 7mm RM or 7mm/300Win.
With the 7mmRM, you can buy ammo nearly anywhere. In the 7mm LRH, though there are notable performance improvements, ammo is obtainable in reload form only (and likely harder to source brass).
Another completely different element/tangent to consider is how large a bullet (and to what performance level/lethality) do you really want to use in a 7mm caliber vs what you can easily get from your 300 (not sure which 300 you have...).
As an aside, a big 7mm can do a lot, but a big 300 does all of it and more. A big 338 out-classes both at the longer end of the range (in terms of lethality).... I am a huge "big 7mm" fan - there is only so much .284 can do!!!