This ^ is a very smart thing to do.
Ultimately and in the end, a "smart" Captain would outsmart the trolls by possibly doing this and other things. For instance, as Captain just personally chat to those crew members you wish you keep and communicate to them a plan. One such plan could be to take your ship completely out of action for a while by just cruising around the Caribbean (on the outskirts) where no loot can be acquired. Sooner or later, the trolls will grow impatient and then leave to where...as Captain...you have then the luxury to close that ship of yours to the public and continue to plunder with a crew trustworthy to your cause. (For those crew whom both stay and listen to you throughout such time, these are the type of people you want on your ship whom understand the mutually benefit of a working crew coupled with a patient/wise Captain).
*As Captain of your ship, there is nothing wrong with "testing" your crew's loyalty and/or subordination.