I had the same problem with my P400. The Epson monitor utility will report a 0x73 error. - and I traced mine down to the PW sensor underneath the print head. I had problems with my carts getting “blocked” and tried removing the plugs - and like you ink got dumped into the head and onto prints. The drops that landed into the paper were huge and I assume were struck by the head - and getting into the recessed sensors. I first did the piezoflush papertowel in the platen cleaning trick, which revived my printer - but only intermittently. I didn’t want to take the print head off so I modified a toothbrush by trimming the bristles very short and grinding down the brush head so that it could easily slide underneath the carriage assembly/print head and brushed the sensors clean (I assume so as I couldnt actually see what I was doing). So far so good…
I found pictures of the head in the service manual - you only want to brush the area near the sensors - which are on the left hand rear side of the carriage. You don’t want to brush the actual print head.
Avoid at all costs installing the carts without the plugs - you’re just asking for trouble. I bought a bunch of extra spare carts for when the air vents get plugged up. You just replace the chip with the corresponding one from the bad cart.
I did also salvage one cart by shoving a large needle in the air vent and “scraping” the foam to the side to create a sort of tunnel to the opening on the edge of the cart.