I had the same situation trying to use GUCs. KL operated, DL coded flights JFK-AMS. The agent said Z was available, but that the upgrade was only available if KL coded. They would only process it if the ticket was reissued to KL numbers. They waived the change fee and it increased the fare slightly.
I wonder why KL is releasing inventory on its flight numbers but not the delta code share, especially when these certificates can be used either way.