you could open a new cartridge, run the strong clean, put back the near end cartridge, & use it up...
..I know I did that once, but I think it didn't beep for the ink end after doing that... it just dropped out, so maybe it's a bad idea. In my case it didn't ruin a print (happened on a small test print) and didn't get air in the lines... but had me worried for a few minutes.