What are you actaully measuring with those 4" and 3+" numbers? Base length? depth? http://www.futuresfins.com/en-us/fin-school/template
Get some either solid fiberglass, performance core(what fcs calls the hex looking core), or fins with carbon in them. Those will be much stiffer than the plastic fins, I'm assuming that's what the stock ones are if you think they feel flimsy.
With the power that the kite generates going to a inside foil isn't going make as much difference as if you just surfed two identical fins of flat and inside foil.
50-50 trailers are going to be more "stable" than a flat foil, a 80-20 somewhere between a 50-50 and flat foil.
I wish that there was a Futures Controllers in a FCS double tab, well not for long as I'm making myself some, I think those would kick as for light wind boards for their increased area. Also I would be interested to see how bonzers would kite...but now I'm going way beyond what you asked.