I wonder how well it would work if someone bypassed the cartridge and just hooked the dishwasher directly to the two giant external jugs, like one of those external CMYK ink tank systems for fancy printers.
That's true. I suppose keeping track another way might offset the added annoyance of the "rewind" routine (attaching another device, connecting USB for power) when refilling the reservoirs. Personal preference I guess.
Replace PCB with your own one having MCU with buit-in EEPROM. Add a tiny push button (or just two copper pads), pressing/closing which will dischage a capacitor indicating "need to rewind" to an MCU. When counter is zero, you take off the cartridge, pour in all necessary chemicals, hold the button for a while and put it back into the machine.