So far the best heavy frigate I found was a speed 14.7 with 5400 HP, 340 crew (as shown on stats, once full perhaps 380-390), 50 32lbers cannons, and 5200 cargo space.
The crew was rather low so I didn't go for it. But if you want a nice little suggestion, autosave then autoreload in the shipyard. But here is how you do it:
BEFORE you open dialog, auto save, then speak to shipyard man and see the ships available. Keep reloading until you find something you like!
I also do this for taverns, except I stand outside the tavern without visiting it for the first time upon my arrival to a port. Then autosave, then enter tavern and keep reloading until I find treasure pirates or appropriate officers.
Unfortunately this doesn't work for governor missions, but it does sometimes give you alternate destinations for one mission only: Sneaking in cities. Can be Caracas, Havana, etc.
All other missions, you can keep reloading all you want but it won't change a thing!
Bankers, street merchants, and shop owners also before you open dialog for the first time, you can save then reload to show different varieties and amounts.
I also do this for bounty hunters who are too strong for me, keep reloading until I can choose the middle option successfully and have them mistake me for someone else!