My proposal is that instead of chyen being kept track of by a single number, the character's cash should be kept track of by bills and coins instead. For example, instead of having 2452 chyen, JoeBaka might 'count' and see "You have 3 five hundred-chyen bills, 9 hundred-chyen bills, and 52 chyen coins."
To pay someone, the character must count the money in their hands manually, for example:
to Joebaka A pint of beer please.
JoeBaka [to You]: That'll be 67 chyen, chummer.
to Joebaka Alright.
cash 6 10
cash 7 1
Shortchange could work the way it used to, with higher risk of failing the more the number stated differ from the cash actually in your hand.
Instead of picking a percentage of a person's cash, pickpockets may instead pick out 2-3 of the highest denomination currency the victim has. I mean, it can't be that easy to pickpocket someone with a pocket full of coins.
NPCs could be given the power to make changes as necessary, and bars could have a change machine for bartenders to sort out changes for the customers. This way, people have more reasons to duck into bars and buy a drink in order to ask for changes to be made.
This will also make topside's usage of cashless transfers much more preferable, and might even encourage some Mixers to hustle and make Red Central go cashless.
Also, just in case somebody thought I'm kidding, this suggestion is entirely serious.