Have you tried making the pate into its own gravy? I add a couple teaspoons of water and mix it well to make a thick soup. Also helps if it is warmed a couple seconds if it is cold from fridge.
You know the freeze dried treats? Sometimes my kitty is occasionally picky, even with her low carb she eats all the time. If that happens, I take a couple of the freeze dried salmon or chicken treats and crumble them up like dust and sprinkle on top, then she finishes whatever was left in dish.
The suggestion for mixing with a lower carb to bring the total carb count down is a good idea too.
13% is more of a medium carb, there are a lot worse, so it is not terrible until you can get him on something lower. But it will lower his sugar more once you get him on lower carb food, so doing it gradually is a good idea also.