We know the boundaries of each empire, and can make guesstimates of each population. Weigh each claim by how long they held it, and the population of each historic state at the time, not the modern successor state. So the centroid of "ownership" would move across South Asia over time (I doubt a weighed centroid would ever leave South Asia). Advance the clock, and the centroid would advance from Southeast India to the north over time. Once the clock reaches the point at which the British ransomed it from Duleep Singh, award it the successor state of wherever the centroid is.
Well, it was defacto owned by Gulab Singh at that point (who was basically his own automous and honestly pretty evil warlord - fun fact, my mom's side of the family is directly descended from his top general and my dad's side of the family emigrated to British India because in the 1800s they were mere Pahari peasants who were required to partake in forced labor for Raja Gulab Singh's family, and resettled on a portion of land that was part of a massive land tract given to a major Zamindar/Feudal Lord who supported Duleep Singh and thus lost it after the war). And the key question then is, who is the successor state? The Sikh Empire's successor state was the British Raj and the Princely State of Kashmir and Jammu's successor state is - oh wait, 4 wars, ethnic cleansing, and a 40 year insurgency occured over this question).
Sure, not in dispute. The point of the exercise is to recontextualize ownership of colonial spoils as the heritage of the colonized people, rather than the personal property of the monarchs involved, or the successor states of an empire. Indeed, I would broaden that to include all wealth plundered from the people, including by their own nobility. If the goal is to restore the diamond to the people who have had the greatest claim to it, it's not an impossible task to determine where their descendants currently live. If we seek to consider to simply restore the diamond to the last royal claimant (and their successor entity) before British hands entered the long relay of property ownership, I'm not sure much is accomplished.
The issue is colonial people in South and Central Asian history is weird because just about every South and Central Asian state (the Durranis, the Sikh Confedracy, the Sikh Empire, the Mughals, the British Raj, the Maratha Empire, the Delhi Sultanate, etc) was a federal system with castes, clans, and ethnic groups being given varying levels of self governance [0][1][2]. So when you say colonial people, does it belong the people of N state of the no longer existing country called X or M state of no longer existing country called Y. Successor States are an actual legal concept which remains a grey area to this day.
On top of that, both Pakistan and India made themselves successor states of princely states in the 1970s but it's still a murky gray area from a jurisprudence standpoint as cases are still being litigated, as the associated federal-local level deliniation is still lacking. Welcome to the legal world.
What does the legal self governance of any single historic state have to do with the question at hand? We have a fairly reasonable model for the people who constitute modern states, and how they were associated in historic empires. So even if the Persian Empire subjugated parts of modern day Armenia and the Persian Empire held the diamond for a while, do we seriously think the Armenian people have a serious transitive claim to the entirety of the diamond? A lot of the contenders you've raised can certainly be wilted down.
South Asian colonial history is no more complicated than anywhere else in the world. Nor at any point have I deferred to the legal inheritance of successor states.
Consider for example the Elgin marbles, claimed by the British from a section of the erstwhile Ottoman Empire. Do we seriously believe any of the successor states of the Ottoman Empire other than Greece should claim them? If the goal is to restore the marbles to their "home", the answer to where they should go is easy. Yes, the diamond's history is more complicated, but not impossible to figure out where it's "home" should be. I've offered just one possible model, based on a collective ownership model, and weighing it by the factors such as how long it rested in each place.
