Mike, I am in no way trying to dis the 375 RUM, but in an attempt to be objective, my opinion is the Lapau case offers a lot more for reasons stated. More powder in a shorter case with superior brass. I've never worked with 375 brass but the 300 RUM brass looses it's pockets in about 5-6 firings at max pressures. Maybe I'm wrong, but I'm guessing the Lapau quality and strength exceeds the RUM's. More powder will mean more velocity and a shorter case means a shorter magazine friendly COAL. All plusses
Mag guy, You could build the Lapua on the 700 but with the bigger bolt face you would probably be pushing it to close to its limits. I'll let the smiths comment on that if they jump in. I know with my 300 RUM build I replaced everything on the 700 donor except the receiver itself. The 375 RUM is a good cartridge but the Lapua will get you farther down range.
As for projo's, you might consider these...
They have a little higher BC than the SMK's and you will likely be able to get them down the bore quicker because of their bore riding design.
Good luck with your project!