I certainly agree with you that sorting makes sense, and that sounds like a logical algorithm. I think 4Hz, or even 1Hz, is wildly optimistic though. 100,000 bills is bags and bags of cash. You're going to be spending a lot of time dealing with the envelopes and folders and things.
You're certainly not going to be able to make 10 piles of 10,000 bills each in front of you. As soon as you get more than a few bills in a pile you'll need to spend time straightening them, putting them in envelopes or whatever, pulling more bills out of the bags, etc. Not to mention resting your hands and eyes. You could make it easier with cash trays or something to keep them from flying all over the place as you sort, but even so, there's no way you're going to be firing out more than one a second continuously for hours.
I wasn't suggesting making 10 piles; I was suggesting making 100 piles. (With cash trays with cubbyholes you could reasonably do 1000.)
You can take, say, 300 bills in your off hand, use your thumb to flip each new one, and use your good hand to take it from the handful and place it into one of the 100 piles within arm's reach on the table, according to the digits you saw on it while your hand was returning from placing the last one. If you're doing this in 800ms, then when your hand is empty, you have spent 240 seconds and can easily spend 10 seconds picking up and riffling another 300 bills, bringing you to 270. After two hours of this, you have sorted 8000 bills into 100 piles of 80 or so bills; you should now take a ten-minute break. After another two hours, you should spend five minutes putting those 100 piles into envelopes so they don't fall over, and take another ten-minute break. (Or a half-hour break for lunch, which I wasn't counting as part of the workday.)
That's what 1Hz looks like, and I think you can get to that speed pretty much right off the bat, especially since accuracy is not crucial here (unlike in almost all cash-handling operations!). And yeah, 4Hz sounds "wildly optimistic", but it isn't, really. That kind of speed improvement for manual movements with experience is common for assembly-line tasks. Watch the knife movements of a sous-chef on video, and consider that every one of their movements is irrevocable; they don't get a chance to spend time straightening crooked cuts.
