Thanks for the info! I think I would have to destroy it to open it, but someone tells me it sometimes works to flood isopropal alcohol in it and hope it reaches the needed area. So that is what I have done. (edit: it did not work for me, nor did compressed air)
The board gives no part number if I need to replace the encoder. I wonder if I can hack this by soldering wires to the contacts of the encoder and touch two wires together to make it register a rotary step.