I would agree with you on the MM#622. Has anyone ever found a cartridge with this bullet in it? For all we know it may be a French import, made in Vicksburg like you said. Can anyone ID the troops that used this ammunition. That would be a good starting point for research.
The MM#622 Bavarian Sharps Variant that Tom Stelma has listed as 02-087 is a post war .50/70 Trapdoor Round. That exact type has fooled people for many years. If you look closely at TS02-087 and other examples, you will notice that 99% of the examples recovered are fired. The original bullets were housed in a copper metallic casing and were internally primed.The majority of these were produced at the Frankford Arsenal. There are a few non fired ones that have come out of trash pits at early Indian War sites out west. For this reason, non fired examples do command a premium among Indian War Collectors.