Great Bill! Thanks for the clarifications! Man, I swear that photo of the breech looks like the barrel is already down in the stock! How'd you do that?
Well, after some thinking on this and digging into the order bin there was a flash of bright light (insert blond jokes here) and I realized that you have a York Light kit run in an "A" weight barrel. We don't have a specific pattern made for that barrel so the stock carver basically is doing a custom stock. To accomplish the machining for this size barrel the carver will line the B weight pattern with a few layers of masking tape to shrink the inlet. If he added one layer too much you end up with a very tight fit. So, yep you'll need to remove a little bit of wood and like other suggested I'd start on the thicker side. It's shouldn't take much to get it to go on down into the channel - remember masking tape thickness. Also since it is an A weight barrel you will want it to remain as tight as possible, with good fit, to help stabilize that small and long barrel.
You also will want to pay careful attention to the depth of the channel. Reason being is that since that pattern is modeled for a B weight there is a 0.063" diameter difference between the two barrels will affect the placement of your touch hole liner. So your barrel may have to go an extra 0.020"-0.030" deeper to make sure the liner is centered on the flat and still in line with the lock pan. If you get a moment please let me know if we sent a 5/16" liner or the 1/4" one. I think the 1/4" one will fit that barrel better and will send one to you if that's not what you got with the kit.
Oh, thank you for the kind words too! :-)