I think you were right about the Swiss Vetterli. The bayonet has what seems to be an asterisk, an H, and an imprint that looks like a little wrench on the curve before the blade starts.
The scabbard is for a French Lebel rifle.
The two remaining bayonets with similar sockets but slightly different lengths are both marked "U.S." and seem to be one of the designs that came right before the civil war.