Check out this link:
Look at the "Convert"; "Teardrop"; and "Sweeper".
Notice the curve toward the tip of the fin.
Compare it the the Series 2000 and Formula.
The "curved back" planform is what will make your board easier
Not just a narrower foil, but a foil that curves back.
Higher aspect ratio is OK, but it does not make a fin "turny" and
for easier jibing, "turny" and somewhat "loose" (like a wave fin (the "Enduro" on the link)) is
what you need.
I think we have some "terminology" issues in this discussion:
Rake is an inclination of the leading edge of the foil (back from 90 deg).
Span is the overal length of the foil (from the bottom of the board to the tip of the fin).
Aspect ratio is the ratio of the width (front to back) of the foil to the length of the foill
(or the Span).
Thickness is the thckness of the foil. (There are thick foils and thin foils).
In order to make a fin "loose and turny" the foil is usually fairly thin and the leading and trailing edges have lots of curve to them (like the Enduro wave fin in the link).
Thin foils allow for some "twist" and bend". Thick foils are more rigid and may bend along the span but only twist near the tip. The fin guru's use directional carbon to get the bend and twist to change from the base down to the tip.
Hope this helps,.