I believe the 338 Big Baer is based on the 408 CT but I may be wrong about that, not sure.
The 338 Kahn was developed by Kenny Jarrett a long time ago. I got his reamer design. Only thing I do not like about his is that its a tight neck reamer and requires the neck to be turned. I do not particularly care for neck turning but on a rifle like this not a big deal.
Took a while to figure this need out. At first I was pressuring out at 2950 fps and could not figure out why as I COULD push a bullet through the fired case neck. Decided to take a thou off the neck thickness and was able to jump right up to 3050 in my personal rifle.
Again, all of my barrels have been very tight Lilja barrels. When I say tight, we are talking bore diameters in the 0.3282" to 0.3284" range which is well under nominal and WILL limit muzzle velocity. THey shoot so **** well though I never have decided to change barrels. Lilja current 338 barrels will run right at 0.3300" as they should but his 338 barrels from 5-6 years ago were running VERY tight.
Certainly there are barrels out there that are just plain fast, no question there. I have seen some barrels produce velocities I simply refuse to report on because I will be called a liar so that is a very real possibility.
My only concern is that Wby brass is not known to be overly strong and in fact quite soft. Several Kahns I have built for customers would have effortless bolt lift and extraction, but then have the primer fall out as the case was ejected from the rifle. This is one reason I went with the Lapua case for my 338 Allen Xpress. Brass is much stronger, much cleaper, much better quality and will **** near match or will match the big Wby with around 10 grains less powder. I am hitting 3000 fps with my AX and 300 gr SMK in 28" barrel lengths. I have never chambered a 34-36" barrel length but from my testing of other 338 magnums, you will see an average of around 15-18 fps per inch over 28" of barrel length so in a 36" barrel length, it would not be strange to expect to see 3100-3150 fps with this much smaller chambering.
IF, and its a big theoretical IF because its not true, but if the big Wby case could handle the chamber pressures that the 338 Lapua could, it would easily be capable of producing 3200 fps in a 34" barrel length.
That said, if the 408 CT parent cases could handle the same chamber pressures as the Lapua, it would easily push 3500 fps and in a 33" barrel length. In fact the old TTI 408 CT brass could handle this pressure and could indeed run up very close to 3500 fps. Different topic though.
Anyway, I am not saying its impossible to see the velocities your seeing with pressures that are not dangerous but I would say its very rare to get this level of performance without running pressures over what the Wby case will repeatably support. As you say, a special fast barrel could certainly be the reason.