True that!
I don't thing you need a modded 3ds to sign a save with the Ase Key because if that be the case Datel would need more 3DS then you can count to resign each save that is sent in to keep up with every thing and they would need to keep adding modded 3DS to that line so i call bull on that they use computers to do it because they have software that does that for them.
I can assure you with an accuracy of 90% that Datel is using a 3DS farm to sign the saves for us.
Keep in mind that Datel is a pretty profitable company so investing in 5-10 3DSs is not a huge deal.
The AES chip can NOT dump the keys (it does not need to) in ANY way so, unless you have a magic way to get a 1:1 schematic of the chip's transistor connections, a 3DS farm is the only way Datel can do what they do.
There's littel room to speculation here, as there are various technological and physical constraints that prevent other methods.