Elections in the UK and Argentina would be needed to make them fair to the disputing parties and would be a matter of how much interest each government could generate and the relative sizes of the populations. This would ensure elections for all interested parties and not just those who share the occupiers view; the latter making such elections a foregone conclusion and, therefore, a pointless waste of time and money.
Disenfranchising the poor was tried in the UK by making property ownership a condition of being allowed to vote; ensuring that the political status quo would be maintained. This did not work because the votes of the poor were needed and to have refused them would have led to revolution. This is why doing the same in the Falklands will not work because those you oppose will see such democracy for what it is - as ersatz as asking a Gibraltarian if they want to be Spanish. This would have the side benefit of letting the Islanders know whether or not the British really gives a damn about them or whether they should simply bite the bullet and accept Argentina as its motherland.
A leaseback arrangement whereby a temporary period of dual sovereignty - to iron out all political problems - would be followed by complete sovereignty for Argentina. this would be generational (eg, a 25-year period) to get the islanders used to the idea.
Otherwise, the Falklands would have to become a permanently militarized dependent zone - like Israel - and similarly supported by a foreign power for a fortune in sterling, all this while Britain declines economically and the EU falters and no end to the dispute on the horizon. Even if enough oil is discovered to defray such defense costs, there are not enough people on the island to withstand a military assault from Argentina. The islanders would then have to rely on the colonial power (the UK) to supply manpower and/or employ mercenaries. The UK’s military is stretched elsewhere and so would not be enough to ensure victory or deterrence. If islanders become rich, would they not wish to live elsewhere?
Any further UK military adventures might give the Argentinians the impression that the UK would be unable to defend the Islands with fewer naval resources at its disposal today than it had in 1982. Either way, the cost would be prohibitive and would absorb much of any oil revenue; making such oil of little actual economic benefit to the Islanders - as we saw in Scotland when it did not devolve from the UK in 1979 and most of the North Sea oil money went to England.
Whites here still want to play imperial games and, even though the Raj is dead, there is still some foreign territory with a tinpot Raj that they can feel godlike about. How are the mighty fallen, from an Empire of 34 million square kilometers down to only 2. This is why so much White emotional illogic is being thrown at this issue because Whites are still whining about the loss of the Empire and refuse to move on and get a life. Whites still think that any part of the world is potentially British - no matter how absurd or difficult the location nor how pointless the effort. This uneconomic attitude is why the Empire declined, in the long run.
If Spain, absurdly, decided to occupy one of the unoccupied British Isles, in revenge for the occupation of Gibraltar, the problems for Spain would be the same. An expensive military force surrounded by a nearby hostile enemy for little economic gain.
The morality and ethics of this situation is simple: Realism and practicality is the only way forward. There is no need to talk about the history of the situation since people then get bogged down in disputes that do not matter anymore - unless you want them to and choose to live in the past when a loaf of bread only coat a ha'penny and you could go to the pictures and still have change from sixpence.
The basic issue here is fundamental, as it was with India: When the Natives get restless, you either have to reinforce the garrison at a cost greater than the economic value of the colony, or leave. Brits need to face a truth they hate: The Natives here are the Argentinians, because it is their backyard since the Falklands are not within UK territorial waters and so not a part of the UK. They are simply the leftovers of a failing Empire. And going into someone else’s backyard to claim the backyard is always going to result in fisticuffs - as happened in so many parts of the former Empire.
(Although the Falklands War could have easily been avoided, it was necessary to fight it to uphold the principle that political disputes should be resolved by diplomatic means whenever possible.)
Few Whites have any practical suggestions to make. In the absence of realism, they resort to flag-waving in the hope this will distract them from the reality of the situation: The British Empire is moribund and became so because the costs of garrisoning it got too high to justify its continuance. Only by accepting this simple fact can the future prosperity of the Falklands be assured, since it will create attempts to live in peace with the Argentinians rather than the demanded for a continuous state of war. And war economies - like that in Northern Ireland - provide prosperity to no-one because of the inordinately high costs involved in terms of lives lost and money wasted. Defending the falklands is simply impractical. Jingoism is a desperairing recognition of this simple fact. The Argentinians benefit from pressurizing the British here because the latter then have to waste billions of pounds every year to garrison the Islands - money the Argentinians do not have to pay.
This is the reality of the present situation - there is no other. Anything else is just jingoism and national chauvinism from people who have nothing substantive in their own lives about which to feel justly proud. A typical attitude of post-imperial ennui and gloom. Britain loses nothing from handing over the Falklands to Argentina and may even gain an understanding of its declining place in the world such that corrective measures are taken to form a new polity based on trade. Not very likely since every Empire that died, never recovered. But you never know, the British Empire could be the first.
Imperial mindsets live in an ideological fantasy-world where human lives are statistical abstractions to be forgotten about as soon as learned. No matter how much you might dislike the Argentinians, you are - at some point - going to have to negotiate with them - as was done with the Provisional IRA; even though Western governments regularly claim they do not talk to the very terrorists they do talk with. Someone here needs to get real: You have to negotiate with people whether you like them or not.
Whites also play the race card by supporting Whites in their demand for the protection of the UK government but were never vociferous when Black Kenyans made the same claim when Kenya was a British colony. (In fact, the law was changed to make it harder for Commonwealth citizens to claim UK citizenship - after all of the wealth Blacks generated for Whites, this seemed a mite ungrateful.) A perfect example of how Institutionally-Racist the British Empire truly was, and remains.