I can go with a 4-5k ton ship if it comes with ESSM to start with. Think Absalons with well decks.
I was thinking of something like the USCG's
Bertholf class Cutters, or perhaps the Austal Multi-Role Vessel. Much smaller than the 6300t
Absalon class, these ships would be a better (and cheaper) fit for the job of 'spamming' the pirate-infested waters.
In fact, something like the Project 22460 patrol ships might be a viable option for including in the mix- two dozen or so of these vessels would force pirates to concentrate their assets to make more coordinated attacks. This would accomplish two things: 1.) make smaller groups of pirates give up on many attacks and 2.) concentrate larger groups for easy 'prosecution.'
Much like increasing escorts in WWII both forced U-boats to form wolfpacks and caused increased kill:sortie ratios, forming safe-transit lanes with coordinated patrol forces would minimize pirate effectiveness.