The pit is likely not going to be practical problem. However, chamber sleeving does work. I have had the following:
10-b chamber sleeved to 12-bore
16-bore chamber sleeved to 20-bore
20-bore chamber sleeved to 28-bore
I am juts restoring a 36-bore Lang & Sons hammer gun and will chamber sleeve it to .410 in order that it will actually be useful.
A lot of guns were/are made with wide bores. Some chamber less guns for the 19th century are 12-bore with .778 bores (as opposed to normal .729). The work fine with modern ammo.
I have used the guns listed above with success and Cyril Adams use similar guns very successfully in the live pigeon and ZZ ring.
As practical option, chamber sleeving does work. My observations of patterning fibre and pals-wad ammo is that both work well.