Re: Solved: British-made Enfield model-1853 rifle's buttplate
No, the yankees did not use that numbering-system on Enfield Rifle buttplates. It was applied by the Exporter in Britain. Long ago, I read a lengthy article on the civil war Enfield rifles which said it was only applied on Enfields being sent to the Confederacy. Unfortunately, I cannot currently find that article. But I think it is correct, because the majority of Enfield buttplates we dig on civil war battlefields have no marking at all on them. Seems like we'd find a significant number of these specially-marked ones in yankee-army sites, but we don't. On that note, it's worth mentioning that the State of Massachusetts purchased several thousand Enfield rifles for use by its civil war troops, and marked those Enfields' buttplates with the letters "MA." Those MA-marked Enfield buttplates do not have the British-export numbers on them.
In case you are wondering... I think there are two reasons we have not found a large quantity of the specially-numbered Imported Enfield buttplates in Confederate sites.
1- A great many of the Enfield rifles used by Confederates were captured in battle from the yankees. For example, at the siege of Vicksburg, after an attack on the Confederate trenches in which the yankees lost thousands of troops, the Confederate soldiers taunted the besieging yankees by asking them "Do y'all want to get rid of any more Enfields?"

2- As the yankee naval blockade tightened, cutting off shipments from Britain, several Confederate arsenals began producing their own nearly-exact copies of the British Enfield rifle. Those would of course not have the British-Import numbers on the buttplate.
By the way... the "A" below the numbers on Cdsieg's buttplate means "10,000-plus." In other words, 3396A means 13,396. The buttplate Engraver seems to have decided that a five digit number would not fit properly onto the buttplate's tang.