I recently shimmed the barrels of my M1917 and P14 because they weren't touching and I felt it was affecting accuracy. I made a .020 shim for the 1917 and a .034 shim for the P14. It made a big improvement on both, a 1/4" tighter group improvement for each! I had the 1917 in a sporter stock that I had glass bedded and fully floated. It never seemed to achieve the accuracy that I was trying for. It shoots more accurately now in the full military stock with the front of the barrel supported than it ever did in the sporter stock.
Where are you placing your shims? At the fore end or the receiver?