Broughton and Bartlein are pretty much the unofficial leaders of the pack on 6mm barrels these days. But I'm not sure the wait and the extra cash will show up in your targets. I'm sure all of 'em shoot better than we do. I've been researching for a while now and one thing I can recommend is going with the 1:8" twist. That configuration will handle 105 grain projectiles, and your light bullets with ease...certainly the 95s. The tighter twist is required for the heavier bullets and will shoot the lighter ones. The slower twist will not shoot the heavier bullets so does not offer the same flexibility. Go with the tighter 8" twist just in case you decide to get into some longer range shooting that calls for heavier bullet. Your stock is likely set up for a Remington Heavy Varmint profile. If you search the barrelsmiths websites, you'll see that they all make one that copies that same profile. Some even indicate which barrel is "their" Rem Hvy Varmint. They have drawings with the dimensions of the barrel contours on the websites too. You can use their line drawing to compare to the inletting on your stock and figure out what will fit, or if you need to have your stock modified. I can tell you that Greg Tanel in Colorado is a good gunsmith. Another is American Precision Arms in GA, but I'm not certain they're taking any rebarreling work.
Do some diggin', that's half the fun. I'm getting ready to send a pile of components to a 'smith for my .243 build. It will include a Broughton 5C 6mm 26" barrel w/1:8" twist, in their 5.75 ocntour (Rem Hvy Vrmnt), Rem 700 SS action, Manners T5A composite stock, and an assortment of other items I've spent nearly a year putting together. I'll be glad when it's finally a gun.
Good Luck,
JB in NC