Code says you may submit your renewal request up to 180 days before expiration. Would that put you in a window to submit your renewal while you are still in KG, then just change the address after the new one is issued? (You may need to add a note asking them to hold it for you rather than mailing it to your old address.)
If that does not work, I would print out the portion of the law that covers renewals, and ask the clerk (not the ladies who work out front) to look it over and show you where it says you have to submit as new.
This does bring up an interesting sticking point, if KG does not require prints, but the city does, then that would seem to be a slight discrepancy in how the law handles renewals after a move.
It is still on my list of things to do to mount a concerted effort to get the city to drop the prints requirement.