Have you bedded the stock? I can't blame you for giving up, I did the same thing with my 270 WSM. I put a Pac-Nor barrel on it and now it's a tack driver. Since you're already set up to load for the 30-378 I would consider putting a match-grade barrel on there and sticking with the same cartridge. .338s are fun though and I think they're a better use of all that powder.
@Yobuck, I'm sure the 300 Norma would work really well on a Mark V action. There's plenty of room to run Lapua brass though, so based on length alone there wouldn't be an advantage to the Norma. I realize that you can get factory brass and dies for the 300 Norma however, so that's a good reason to choose it.
One thing I've noticed about my 338-378 is that its very finicky. Not that its hard to find a load for it, but this gun will let you know if you're in the ballpark or not. Typical load development for me shows groups ranging from 3" to under 3/4". I actually like this. It makes it easy to zero in on a good load and rule out the bad ones. I've also noticed that if my rest isn't solid I will get erratic groups (mostly vertical stringing).