It's an interesting puzzle for sure. It looks just like a bad print head but if you are saying you have replaced both c/lc heads then that does point to an ink delivery problem.
The fact that your print head refills while cold makes me think there is a heat related issue such as a hose line kinking when hot, or fitting coming loose. Since you haven't mentioned any puddles of ink pouring out of your machine makes me think it is on the pressure side of cartridge. You can tell if your cartridge is pressurized by trying to remove the cartridge prematurely (don't do this while it's printing obviously) while the printer is awake and ready for a print. It will be difficult to pull it out when pressurized. If the cyan cartridge just pulls out then I think you have found your problem.
I would remove the end covers (starting with the ink cartridge side) and inspect the pressure lines, puncture needles, and solenoids which discharge and regulate ink cartridge pressure.
If its all normal then I would look at the feeder assembly on the print head side and make sure it isn't clogged, and that all delivery nipples are looking aligned and not pushed back or crooked.
Last, but probably the first thing is to clean the head carriage contact terminals for all heads. Hopefully you have the tool for that and the cleaning pads for the tool. If not then you may want to search for an alternative cleaning method since I don't think the provided cleaning pads are covered in alcohol and I am not sure if the contacts can support an alcohol cleaning.
It goes to show you how much has really changed between the HP Latex 2550/2650 and the 260. The 260 warns you when something isn't right where as my buddy with his 2650 tells me he never sees a thing until it's too late.
