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In this sheriff’s office, like several other law enforcement agencies, ranks jump from junior officers (lieutenant, captain) straight to flag rank (1 star for chief deputy, 2 stars for assistant sheriff, 3 stars for under sheriff, 4 stars for sheriff). Just seems like someone really wanted to dress up in a general’s uniform.
At its core, the Gilligan’s Island model relies on the lagoon as its main source of conflict – something floats in, the castaways have to deal with it. The lagoon remains constant, the things in it change. Most ship-based Star Treks are anti-Gilligans Island shows in so far as they are what’s floating into someone else’s lagoon. They remain constant, the lagoon changes.
If anything, I would say DS9 is the better Gilligan’s Island analogue, with the wormhole acting as the lagoon.