This is the first I've heard of the 7mm LRM... maybe you could fill me in?
On the 7 Dakota vs the 7-375 Ruger, I have just gone through the same decision process withe 300 Dakota vs the 300-375 Ruger and picked the 375.
I think both have very well designed cases and they essentially have the same powder capacity but in the case of the 7 Dakota, it is slightly smaller. The 7 Dakota brass is made by Norma and probably a little better than the 375 brass which is made by Hornady.
The problem with the Dakota chamberings is that they are proprietary which makes die and brass selection and cost problematic... which is truly unfortunate because they are great cartridges... and this is why I went with the 375 Ruger parent. Dakota brass is $163 per 100 and 375 can be had for half that.
As far as dies go, Dakota chambered dies are very spendy, but you'll have to get custom dies for the 7-375 Ruger and forming dies. Custom match grade dies from Hornady will run $190 plus shipping, and $22/27 for the micrometer seating stem. You can use the 338 RCM and 300 RCM dies as forming dies for about another $26 ea.
What you save in brass you can put toward good dies.
Now don't forget, you'll have to turn your necks once or twice while forming the 375 cases. So you've got some work involved in getting the 375 to a 284.
The biggest thing that puts me off about Dakota is what they charge for brass.
The nice thing about both these cartridges is they will fit into a Howa/Vanguard and Rem 700 magazine (if not throated real long) with longer bullets vs something like the STW.
Well there you have it... be the first kid on your block with a 7-375 Ruger