I don't see a 375 on their website, but I'd give them a call... one of these days im gonna stop by and try to get a tour, I live 5-10 miles away from their shop.
Look under Contact Us on their website for email. Not every business is "email friendly" so they may not prefer to interact by email.
Also you should be aware that not everyone spends all of their time updating the website. Some people prefer to spend their time actually building barrels.
I would suspect if they build 20mm cannon barrels that they can build you a pipsqueak barrel.
I do not want to speak for Bartlein, but I know of at least one person who had a .375 barrel on order from them several months back (I don't know if that order has been cancelled).