Thanks for the detailed information, this is all very helpful to trouble shoot and resolve your issue.
I have never experienced or heard of what you explain about the cartridge door opening speed before. I assume the difference is pressurization- when all carts/chips are correctly read by the printer, it pressurizes the carts to be "ready" for printing, and needs to release the pressure before opening the cartridge cover. If a cartridge/chip is not correctly read by the printer, it will not pressurize the carts, therefore not need to release pressure before opening the cartridge door.
Thanks for checking the reset chip pins and cleaning the chips (by the way- how did you clean the chip before?). I included a pre-written instruction (which includes things you have already done, but please check everything) below for checking the chips on these carts, if you could please check these things and let me know your results/findings, then we can move forward to get this taken care of for you.
38XX “80ml” refill cart reset chip check: The plastic base of every 3880 reset chip should have three small plastic tabs around the side that hold it onto the cartridge. If any of these tabs are broken or bent inward, the chip will not stay secured to the cartridge, therefore not have a good connection with the Epson chip underneath, which will cause an error. Also, on the back of every reset chip, there should be three metal pins that stick out and touch the Epson chip- the three pins should be equal length for proper contact with the Epson chip. Please check the plastic base to make sure there are three plastic tabs, and if they are all in place, gently bend them outward slightly to ensure they catch and hold onto the cartridge. Also check to make sure the three metal pins are present and equal length. On the front of the chips, please check the gold contacts to make sure nothing is on the contacts that would interfere with the printer's ability to read it- if you see anything on the gold contacts, gently clean them with either an alcohol pad or pencil eraser. After checking all these things, push the reset chips back onto their corresponding cartridges and make sure they are pushed all the way onto the cart for a good connection with the Epson chip, then reinsert the cartridges into your printer and see how the printer responds.
Best regards~ Dana