I must thank you for the numbers but that is a tiny part of the equation, sorry.
The broadside weight of the Essex gives it a hell of an advantage over the Frigate. The Frigate sailing abilities gives it a hell of an advantage over the Trincomalee. The Trincomalee speed and tacking ability gives it ample opportunity in a fight versus the Essex. Belle Poule fits all roles, a very versatile ship and equally capable to the Frigate.
Pirate Frigate cannot be built so it automatically loses against module capability, not are the built in characteristics exceptional being basic at best.
All are solid representatives of the 5th rates, no matter what guns you equip, what modules you decide to Setup, etc.
What is exactly the problem ?