I would say aspirate the ink overfill amount at the cartridge output orifice using the provided syringe (you do this any way to prime the cartridge), and put the aspirated amount back into the ink bottle. Do this until the cart shows the proper fill level?!
I suggest using the filling syringe and use it to suck out a small quantity from the filling opening. I have done this a couple of times when I was a bit to hasty in filling. No problem and works fine on my 3880.
What exactly is “overfilled”? I always fill my 3880 carts to the brim with no problems. But yes, if you want the level down a bit, sucking it out the output port is clean and easy.