Now, I don't remember who the maker was that I got the 'Replacement Barrel' from. I'd need to search... It wasn't from S&W.
The barrel on the Left is the Factory Barrel and the one on the Right is the Aftermarket Barrel that they said 'worked in other people's Shields'.
Perhaps a forum search for 'aftermarket Shield Barrel' (linked with my name) will bring up the thread.
Edited to Add:
Found it:
Shield Conversion Barrel TR Enabling was the company I tried.