Yes, I tried supping my Serenity on a flat water lake with different fins : 32 cm, 40, 48, 54, 70 and 80 cm. No matter the fin lenght, she is still unstable and tippy solely because of her rounded hull bottom. However, big fins act like an anchor while supping, so I would advise you to try her with your smallest tuttle box fin you have at hand.
In contrast to the Serenity rounded hull bottom, the K15 hull bottom is a bit flatter, the center of gravity where you put your feets is lower due to the deeper deck, and K15 weights more than the wood Serenity. These features make the K15 a better balanced SUP than the Serenity, but still quite tippy for a complete SUP novice as myself*.
If you plan to use your Serenity once in a while as a SUP on flat water with no wind in sight, that's OK. Even as a kayak for kids. If you want to be serious about SUP, better get a dedicated SUP : allround, cruising or racing, choice is plethoric...
A last note of caution: always wear a leash with your Serenity while SUPping (a 10' lenght attached to the middle handdle bar is just fine). In case it gets suddenly windy (1 Bft is enough !) and you fall into water, the Serenity glides and goes away from you very quickly, pushed by the gentle wind because of her sizeable thickness and overall dimension on the water. Remember, she glides effortlessly, with but without you on board as well...
(*) for a report about my SUP novice skills, please see the SUPer 10'0" report on the french forum : http://www.star-board.com/forum/showthread.php?t=15464