I tried to follow the spirit of the challenge and not look for a way to bend the rules in favor of my fleet, just going with a single extra-action gunship and 2 treasure runners. I worked up similar builds for each pirate lord and they all came out pretty competitive. The fact that we can use forts tipped the scales in Calico Cat's favor. Her connection with L'Argus allows the use of the Paradis de la Mer.
With this fleet she has a very competitive gunship:
(Lady's Scorn: S+S+S move, 4 2-point equivalent cannons, extra action w/ reroll, exploding shot, Eternal),
an extremely fast explorer:
(Zephyr w/ L+L),
and a speedy follow-up treasure runner:
L'Argus(S+S+S w/ helmsman) that can't be shot within S.
Since neither treasure runner has much cargo space, the key to winning will be getting enough treasure quickly enough to build the Devil's Maw and Paradis de la Mer while most of the starting treasure is still on their islands. This should be accomplished by no later than turn 4 unless the wild islands are too widely spaced, but that would be a problem for most other fleet's treasure runners as well. These forts will provide the advantage in cannons and damage absorption needed to tip the scales of victory in my favor. Devil's Maw can also recycle any crew lost, and having the forts around to occupy the opponent's gunship will be very helpful if the Lady's Scorn has to take advantage of its eternal keyword and regenerate at home.
Dead Man's Point will come into play if the Zephyr (who only explores until all 3 Forts are built) makes it to a third wild island alive and can hang around long enough to have enough treasure on the HI to build the last fort.
Add in Homemade Flag in hopes that L'Argus will find it and become immune to cannon fire.
The 6 extra points are from the two questions and pointing out another crew.