Looking for a barrel for 322 Hornet

I have a model 322 that is supposed to be a 22 Hornet, but the chamber has been redone to what we think is .222. The barrel has not been remarked, but the .222 Rem is the only cartridge that comes close to fitting. Nothing else is changed from the original Hornet configuration. I've been looking for a replacement barrel in 22 Hornet, but have not found anything. I've even considered having a blank threaded and chambered.
The 322/340 series is the same system as the 110/112/114,etc..., but different diameters. The 110 series small shank is 1.055" at the shank threads, and as best I can tell, the 340 series is .855 - .860 at the shank threads. The other issue is that the 340 series rifles use a cone breach vs. the flat breach face of the 110 series. I really don't want to change the extraction mechanism on the 340 to work with a flat breach face.
I constantly check gunparts for the "unicorn" barrel, but no joy so far!!

Any help or ideas are welcome!!

Don

The coned breech was only used on the Hornet and other rimmed cases. The .222 barrels have a flat breech face just like a 110.

In my case, on this rifle, it is still a cone breach - but an owner in the past has reamed out the chamber for .222 Remington. I just want to replace the barrel with the appropriate original in .22 Hornet, and I'm hoping someone here has one, or knows where I can get one (for less than having a custom barrel done!).

None out there?
Or does this area just not get much traffic?

Still looking.