I rather instead fancy letting the Brits occupy a remote island, but unlike the Falklands where they had the support of the local population, in this case where the citizens are in absentia accused of being stateless persons and refugees in other countries (those host countries bound by a UN Convention on Stateless Persons). A standoff of sorts.

The point was let them violate the sovereignty of Pitcairn if they want to, under the watchful eye of the people of the world. Let them try to spin their propaganda on the airwaves, while the truth leaks out through 100s of anonymous blogs on the new anonymous internet. Let the Brits destroy the peaceful lives of the descendants of the original settlers.

Maybe along the way, hackers (such as Anonymous) with new untraceable drone technology that sinks every British supply ship that tries to resupply their occupying troops.

You are highly underestimating the power of programmers and math in this coming Knowledge Age.

If ever 100,000 programmers and mathematicians turn against the 0.001%, the 0.001% will be burnt toast.

I think also you perhaps ignored the part of the OP that talks about trying to negotiate treaties with the competing claimants on sovereignty, e.g. some treaty by which the Brits retain some influence if they back off from a direct confrontation. TPTB have to calculate their potential losses from a direct confrontation. The point is to make it less costly for them to accede some sovereignty than for them to try to bully their way.

Imagine the lone student standing in front of the tanks at Tiananmen Square that led to the fall of the Iron Curtain in China.