.677" is exactly 15 gauge - 466.7gr. for a round ball that size according to my chart. for a round ball for that bore, I'd use .650" ball and a .020" denim patch - which would give .0065" compression per side - an easy loading combination with either WW or pure lead balls.
You can get the proper sized wads from Track - they list the sizes of the wads. Your barrel size is almost identical to my brothers Manton 15 bore - his is .675" & I think he bought 15 bore wads, which measure slightly oversize at around .680", which is perfect for the 15 bore.
His gun is cylinder bored same as yours will be - best load for us is about 70gr.2F and 1 oz. shot. Hard card on powder, then 1/2 cushion, shot, and thin overshot wad.