Except at least some of the printers will refuse to work with anything except genuine HP ink cartridges.

The solution is never to have anything to do with Hewlett Packard, especially printers.

People that sell third party ink are unfortunately opening themselves up to getting lawyered out of business. I only have anecdotal evidence from my own experience, but it wouldn't surprise me if the big boys intimidate 3rd party ink sellers (which are always smaller companies) with legal threats and the little guys either give up or go bankrupt from paying legal fees against a megacorp that drags out litigation as long as possible because they have lawyers on retainer so might as well put them to work.