CDUSMC, I had a very nice 219B that had been rechambered to .219 Zipper Improved. On discussing this with several gunsmiths, I had it relined to .25-20 WCF because nobody had a liner in .22 Hornet cal that would fill the chamber of the wildcat (which is based on the .30-30 case head).
Now, you don't have THAT problem with a 16 guage bore to reline to .225. But you will have to have a custom liner made from a .224 barrel blank of the correct twist, and that can get costly unless you can find a friendly machinist who will do the preliminary turning work to fit the blank to the shotgun chamber and bore. My gunsmith who did the reline wasn't interested in doing all that turning work; he wanted to use an already made-up liner, and did for the .25-20. Your 'smith will also have to have a .225 Win chamber reamer; not all have them and renting one is an extra $60-70.
My ultimate reason for going with a .25-20 reline was 1) I like the cartridge and already load for it, 2) I didn't need another wildcat to buy dies for, and 3) the most potent reason, I'm more than a little bit leery of added pressure beyond the ctgs. I know are safe in a 219, i.e. the 30-40 which Garnett has mentioned, and the .22 Hornet or perhaps the K-Hornet, which Frank de Haas used in his. These are very sturdy little guns, but not Ruger #1s or Win Hiwalls.
Just my $.02.