if aiming for 12-13 knots with a 12m inflatable kite, I would think a strapless board would be more fun, since jumping might not be the most exciting (if even possible?) with this kite and wind strenght.
for very low wind, I love the Door 64, but as I don't own one, I have mostly been using a 6'0 fish surfboard (flat rocker and wide board) and recently gave a go to my 9'0 malibu and have to say that the low end on this is VERY low thanks to the huge volume... pretty fun but challenging to turn though!

. I think the bottom end could be slightly better on the longboard than on the Door 64 due to the floatability of the board, which can deal with a few seconds of zero pull from the kite... and I find it to be a good training for improving surfing skills as well.