Thanks so much John, Ernst, and Dan!

Sorry for the slow reply, there was a nationwide internet outage and then I was driving across country all day yesterday.
John, you're probably right about "clone heads". I probably misunderstood the owner. They basically said "it needs new heads and inks, they tried some cheap stuff they bought online, and it didn't like it". I assumed that meant heads too, but I think you're right, it's probably still hp heads and just non-hp ink.
Ernst, great idea using those caps that way! Wish I still had those. In my case I think it is probably easier for me to buy the priming syringe pump that LPS sells.
Dan, I'm waiting to hear what ink the owner used. It sounds like it was a bad match and it wouldn't print for them. I'd rather just remove it, and that way I can rely on consistent print profiles, etc.
Originally I assumed I would install new HP ink, then use the syringe to pull out the old ink until the new ink reaches the carriage, which is kind of a guess how much to pull, then install the new heads and run a bunch of diags, purge plots, etc until the output was consistent. But now I wonder about this idea: what if I use the syringe first with no ink carts installed? I would pull the old ink thru until I get nothing but air. Yes the lines are now full of air, but ideally almost empty of old ink. Next I install the new hp ink carts and then use the syringe again to pull the air out until the new ink reaches the carriage. My understanding is this is the same method as priming a printer after new empty tubes are installed. By using this method it could reduce the potential for any mixing of the old and new inks in the tubes. Also I won't have to guess how much ink to pull, it will be obvious when the new ink reaches the carriage. That could help reduce waste of new ink.
I could do the initial test/purge prints with the old heads if they are still working, and then switch to the new heads. I like the suggestion to keep the old heads afterward in case they are helpful for stuff like this in the future. I've had good luck recovering blocked heads in my Z3100. Only the troublesome MK-R had to be replaced 3 times..., and now that I recently learned how to open and clean the capping station, I think those MKR "failures" were preventable.
Thanks so much!
