IMHO, the fact that you don't really like anything about the rifle might be reason enough to stop where you are. Any time/effort/money put into the gun, and especially if it doesn't help will just make things worse. And, if you do something that turns it into a sub-MOA rifle, would you be willing to carry it?
Every '06 that comes through me gets 57 grains of IMR 4350 and a 165gr bullet to see if it has potential. Pretty much what everyone else is saying. I think it was Jack O'Connor who would joke saying that if a 30/06 won't shoot 57gr of 4350 with a 165, you need an exorcist, not a gunsmith.
As far as the Grand Slam goes, I have exactly one case of experience with the new ones. My 1979 era Ruger M77R in .243 always shot about 1 1/2" to 2" groups for me when I was a kid. It got semi-retired, then I got really good at building accurate loads for just about anything. I took out the old rifle and tried many recipes with Interlocks, Ballistic Tips, Partitions, etc. One to 1 1/2" groups were the norm. One day I dropped in the 100gr. Grand Slam and my groups instantly shrunk. With the same hand-me-down Weaver K4 that was mounted in 1979, I can do 3/4" or better most of the time, and I've watched my son (with apparently better eyes and coordination that me) put 3 shots inside a dime at 100 yards on a couple of occasions. Again, that is a sample of one, but I have been impressed enough with that bullet on paper and game that I bought some for my semi-finicky .270 just to see what happens.
