Ouch……Here is the predicament you may find yourself in. Most of the more well known aftermarket injector folks are just changing tips now and you actually keep your original injector bodies. Even Diesel Dynamics is that way. If you buy their "injectors" versus their "tips", they still require you to send your injectors in and they put new tips on and send them back to you. A lot of these places are not repair facilities, so they may not notice that an injector is sticking and what is causing it, or may tell you up front that they can't guarantee they can fix it. Most all of them don’t have the equipment to test our electronically fired injectors, so there would be no way of knowing if it is fixed until you put them back in the truck. It would suck to get your injectors back with fancy new tips only to have the #6 sticking still.
There are a few, like Jannety, KAX, DPU, that still swap out the entire injector, but then you would be passing your problem on to someone else and likely be hunted down when they figure out you sent them a bad core. I would imagine that happens a lot and they have a "good faith, good repair" clause on their core returns that you agree to and they have a way of dealing with it, which probably wouldn't be in your favor either way.
There are a few injector repair facilities like Industrial Injection and Valley Fuel Injection that rebuild and resell our injectors as well as performance (honed) injectors. If you could mark the bad one they can absolutely tear it down and fix the problem, for a fee of course, then upgrade all six and send them back. This would probably be the safest option for you. They also sell reman injectors for around $350 to business and around $500 to the public.
If you want EDMs and not honed injectors you may try talking to one of F1 Diesel's distributors and see if Don would be willing to take a shot at repairing your bad one. Pretty sure he could, just would be a matter of whether he has spare parts on hand and is willing to spend the time. He is not really running a repair facility so he may not want to fool with it. He usually insists that the injectors be in good repair before he upgrades them.