I've quoted you're post but this isn't entirely directed to you...
I think my first response would be to say that if you test positive you shouldn't be traveling at all..... you shouldn't be on a plane, cab, airport, etc... where you can infect innocent people if there is even the slightest chance of a positive. you should be self-quarantining. Get the next test for sure, make sure....... but I'm gonna say if I'm having a party and someone comes to the door and says "Yeah, I have a positive Ebola test, but I don't believe it..." are you going to let them in?
Refunds, rescheduling, etc... are the domain of the travel companies but bringing COVID to an island isn't part of what you paid for.
If you test positive (even if it's a false one.... you shouldn't be in a cab, in a plane, in hotel, on an island where you inflict massive harm.....) until you can prove that it's a true negative.