Timmyatneb,
The list that I have for factory barrel twist rates states that the Browning uses a 1:10" twist rate for their .243 barrels. However, you can double check this by using a ball bearing cleaning rod with a snug patch.
My guess would be that your twist is slower than necessary since a top end load with the WSSM needs at least a 1:9.3" for these longer VLD bullets. Bartlein makes mine in 1:8.7" for all of the 6mm barrels I use.
I also suggest that these VLD and VLD Hybrid bullets take a little more care in tuning loads than do the standard boat tail bullets. What may start out shooting mediocre simply needs more work with seating depth and less contact with the lands.
As far as locating a gunsmith is concerned, what is your approximate location? I can suggest several given the locale. The Browning can be blueprinted and barreled just like any other bolt action rifle.
If you want to check the Bartlein website, you can try the #4 Bull Sporter as a good compromise to the heavier Varmint or Palma contours. I've used this contour on several rifles for 1,000 yard targets quite successfully.
Regards.