Hopefully, you have adequate proof that the parts are yours.
We had a trailer with a water damaged floor that we returned it to the manufacturer for warranty repair.
The manufacturer declared bankruptcy, and the entire manufacturing facility was chained up, waiting for the court to deal with the bankruptcy.
Our trailer was inside the fence.
We needed to contact the sheriff, prove ownership, and then we were able to retrieve the trailer.
I can’t see how it would be any different for shotgun barrels. Hopefully the serial numbers are on the barrel flats.
FWIW, I’d start with a registered letter requesting this smith contact you.
It could be something like illness that has things bollixed up.
I hope you get a good remedy quickly.
This might be a case where you authorize another member of the site to retrieve your barrels for you to save you having to travel.