Ahoy, matey,
Basically, you're absolutely correct. Hunting pirates is first and foremost a matter of practice. Most of the players prefer, by the way, the 'Kraier' (I do not know the correct English noun for it right now; i.e. : neither cog nor holk nor snaikka) as a (manually operated) pirate hunter - it is solidly armed (if upgraded twice)
and fast
and agile. One can -with a li'l practice- easily outmanoeuvre the clumsier cogs and holks with them. (but) Remember to 'man' them optimally and buy cutlasses at the weaponsmith, if possible at least 1 per sailor.
A general 'bit of advice' : you need more ships. In P3, one can't have too many, only too few
. In your (early) game a pirate hunter squad of 2 or 3 'Kraier' (best : with a captain having high skills in sailing and combat ( = 3 , better more ) ) serves best. As a player, (manual) combat vs the 'blackflags' is indeed easier if the (virtual) captain is good at his job, too
. In times when you do not need them, you can transport smaller amounts of goods or do manual trade w' them.
Finally, RE : missions vs/on pirates : try more taverns. These are randlomly generated and might be available in
any of them. Just keep looking.
Best regards,
d.V.