I don't know if the Drake fins on the '07 iS 111 are the same as the '08, but I have experienced the same thing with the '08 fins (38cm and 44cm).
I too sail in flat water with lots of chop, which means that there is a lot of air going under the board. A little too much back foot pressure and the fin spins out.
The 38 is very prone to spinning out in choppy conditions. Part of this is sailor skill, but a large part is the fin. Once it spins out, pulling it back in is almost impossible. However, I don't think the fins are slow, but you can't be fast sailing sideways.
The 44 is better than the 38. If you have the red colored fins, the printing on the fins is raised a bit, so sanding them down smooth will help. I noticed a slight improvement after sanding. Clearly these fins were designed for down wind slalom, with very little foil in the fin to reduce drag. However, any pressure on the back foot to head up wind (Figure 8 slalom) and you are dead.
Given various reports I have seen, you can't go wrong with the Deb fins. However, I decided to try a Techtonics Tomcat 42, which I use with my 6.6, 7.4 and 8.4. I weigh 79kg. Speed wise, I can't tell any difference from the Drakes, but spin out is rare and if I do push out the fin, it comes back almost immediately.
I looked at the MFC fins, but the surfaces are not smooth because of the lines running through the material. This scared me away. MFC is famous for surf sailing fins, but slalom??
I have read good things about Select fins too, but I have no direct knowledge about them.
Hope this helps.