Ok, I did a little research on calibers, the caliber for the original Creedmoore Rollers as used in the match against the Irish Team and their Rigby muzzle loaders was a 44-90, but not the Sharps version, but the 44 Remington Special. This was a necked case, a little fatter than either the 44-77 and 44-90 Sharps and was 2 7/16 in length, the Sharps rounds were 2 1/4 and 2 5/8 long. This is the most likely round for this rifle Factory loads shot a 550 gr bullet 0.442 in dia.
There is a later (1880) 44 Remington that is a straight case 2 6/10 inches long, but it is a rare bird and is often called a 44-90 or 44-100 Straight depending on bullet weight. It also fires a 0.442 bullet. If this was the round it would most likely be marked 44-2 6/10.
One would want to have a chamber cast made if one wanted to fire this rifle, this would tell one for sure which case it used and if the chamber had been modified, not that uncommon. As far as I can tell, either 44 Remington round can not be made from any other brass and would most likely take a few custom lathe turned cases to fire it as well as a custom mould.
One wonders why both a straight and a bottle neck round of the same capacity? Some match shooters of the era prefered a bottle neck round, some a straight case, Remingtom offered both.
Remington also offered a 45-90 Necked as well as the more common straight cases in 45.
Sharps offered 40-50, 40-70 and 40-90 in both straight and necked cases.