By all means get that chamber casting underway so you know exactly what you have. Making brss or having it made might be your only option.

Calibre wise, .673/4" X .695" dimensions says it's a weak 16 bore or a very tight 14. .677" measures 15 bore, while .693" is 14. .662" is 16, so you see you're in the middle between 16 and 13. 15 bore was a popular muzzleloading bore size in shotguns, especially with Manton, although more normal was 14 with other makers it seems, way back when making the change to ctg. guns.

If indeed the chamber is oversize and it sounds as if it is, you will have to do one of two things, get or make the proper size, or anneal the 16 bore cases you have and fireform them to fit. New, 16 ore brass will admit a ball much larger than your groove dia. as in about .703", so perhaps Tinker is on to something - ie: heavier paper ctgs. or perhaps a 14 bore paper case, the thicker walls handling the smaller ball.

Note the picture of my brass above- the centre row with the .030" denim patched balls actually shoot better in my 13 bore barrel than larger balls (top row) that engrave in the rifling.

BTW - that is a lovely rifle - absolutely marvelous - I well understand Tinker's desire for it - WOW - or OW! - I don't own it.