Satalite scan it
They found cities in jungles and deserts using nasa scans. They should get one of island. I would also do core testing. Say 150 feet in different spots. And maybe even side scan the entire water line of island. As far as the swamp goes their is a special bucket scoop they use down south you could drive right into the swamp. You would have those 3 targets in minutes without pumping the swamp. Instead of spending 10's of thousands of dollars on pumping the thing spend that money getting a swamp back hoe from down south and scoop,scoop,scoop done. I pull for these guys but they think so little. Meaning small this and that.
Go big, satellite ,core samples, side scan sonar. And the expensive ground penetrating system that actually tells you what the heck your dealing with. Then decide where to dig. You should know the battlefield before you get engaged and get your but kicked. If your going to waist money at least be creative. I think their is something buried their. But doing what everyone else did will not find it. And just fore the heck of it bring in a medium. If slaves or pirates dug the shafts I guarantee they got murdered and buried their.