You can chamber sleeve to the original gauge or down on gauge. Going down a gauge results in what in effect is a over bored gun. Hence the gurus tell us that pressure is lower and velocity is greater.
I had a 16 that had been left loaded with two paper shells for what we figured was almost 50 years. Moisture and the paper shells caused the chambers to be deeply pitted. The gun was a Fox 16 with 30" barrels and ther price was right, south of $400.00, "as is". It was so bad, that the original barrels were being saved for spare parts as they were unsafe to ever use as they were. Figured that I might as well try to sleeve them. Boring the chambers out was a fairly easy step. The making the chamber sleeve took a lot of trial and error on the lathe due to mostly my lack of experience. Would have been easier to make them back as a 16 but I wanted a 20 with long barrels and this was my chance. I had a extra 20 Extractor and that had to be changed. If it went back as a 16 the original extractor could have been left as it was. It is one heck of a long range dove gun.
If I had it to do over again I let Briley do it for me. While the second one should not take nearly as much trial and error as the first. But this is a job that they can do very well and I think that their price is very reasonable.