Mike, you are correct concerning the Spencer. I remember seeing the 7th's inventory of firearms before departing to their "Destiny", but I cannot find it at this moment. If memory serves me, there may have been several Sharps, and a few experimental Ward Burton carbines in their inventory but not much chance they were ever carried to the LBH. Although, I have read very early copies (early 60's) of the Custer Battlefield Historical Society newsletter about an article concerning a Ward Burton found on the battlefield after the battle, which I find a little suspect, but that's not to say that it didn't belong to an Indian who lifted it from an earlier encounter with troops.
As far as serial # of Springfield's assigned to the 7th, there is little proof of what was assigned to what regiments except for weapons returned to the armory for repair but we do have a glimpse of what range of numbers were assigned to the 7th and the hottest range of numbers is in the 21000 range as several of these were found at the battle site or carried by Reno & Benteen's troops & returned for repair. But "close but no cigar" is what you usually get with an exact number unless it is one known returned for repair or some other reason to record the number.
It was only after the Little Big Horn debacle, that the army started keeping track of weapons by serial number.