The chances of finding someone not only with a 'XYZ Printer', but someone who resets the cartridges with a (approx) $150 'Gizmo 2' board and a Gizmo Explorer card, instead of a $20 Arduino Uno are surely quite slim. So I doubt you'll find that.
Having said that, the Arduino Uno is a (fairly basic) microcontroller, and the Gizmo2 works fast enough that it could likely be used for the task, but it would involve translating the code to run on X86 and your desired OS (e.g. Linux). That's a porting exercise, and it will involve finding out how to control I/O with Gizmo2, and inserting that code into the Arduino code and re-compiling for X86. It is non-trivial if you've not done this before - and harder still if the Arduino code uses things like timers and interrupt functions, because these do not translate into code on (say) Linux in the same way, so you'd also need to understand the Arduino code intent as you're porting it.
So, in summary, I'm (fairly) sure it is possible, but to do it will need a porting exercise because I doubt anyone else has done it.