As far as I know the ink level in the cartridge has absolutely nothing to do
the level the chip is telling the printer. The chip uses some kind of
mathematical algorithm to determine when you "should" be out of ink
depending on the number of print cycles you've sent to your printer.
I've had many people try refilling a cartridge with a chip (Epson, HP,
Lexmark) that said it was "half" empty (or half full for the optimists in
the crowd) but when the printer showed that the cartridge needed to be
changed you can easily tell that there was still ink inside the cartridge
(by weight and by gently pressing the printhead on the bottom of the
cartridge which allows the ink to flow out).
There are many places that can refill such a cartridge and in the process
they actually replace the chip, just look in your local computer paper to
see who does.
Are you certain of this? I have to admit I've had mixed success with
refilling cartridges, but I've never had my printer just plain refuse
to print with one that's been refilled in the manner I mentioned.
It's possible it may have something to do with my printer being an
older model (a lexmark 3200).
Mostly, if I overfill it, it just dribbles ink causing a mess. If I
underfill it, or don't soak the sponge evenly, I get patchy prints.
By this I mean that I'd end up with a line here and there that has
sections missing from the characters, like you'd get as the cartridge
was running out and the head was sputtering. All of this was to be
expected. As I mentioned, the only weird side effect I got was that
the cartridge level on the driver's meter would always show a
perpetual high level or a perpetual low level (regardless of the
actual ink in the cartridge).
I've not modified the printer in any way, nor have I ever modified the
cartridges, except for a hole drilled in the pink plastic on top for
the syringe. The printer certainly wasn't modified before I got it,
as I bought it new about 4 years ago.