Ownership of the deity.

The deity is a juristic person. Hindus have praan pratishta puja which is a ceremony pursuant to which the deity becomes a legal person. The deity is owner of the property. Someone stealing that property does not become owner or change the nature of the property. Law of adverse possession does not apply to property owned by the deity.

Secondly, mandirs were not lying around like unclaimed lands as in the case of open pastures or forests. They were worked upon by craftsmen and artisans pursuant to a collective manual and monetary effort.

I'd shudder to think of the clients you represent if you can dare to be so ignorant yet arrogant with your views.

It doesn't matter what Hindus consider as a legal person. The deity is considered a legal person because the law in force today bestows such legal personality on it. You cannot apply today's law to an idol which may have existed 400 years ago. The applicable law would be the law in force at the time of the alleged destruction. At the time of the alleged destructuon, Aurangzeb was the absolute ruler and the deity was not considered a juristic person (and even if it was the king could extinguish its title to any property). The SC in the Ayodhya judgement clearly said that just because you owned some land in the distant past doesn't give you an existing and continuing right over it. Such a right has to be recognized by every subsequent sovereign. Neither the East India Company nor the British Crown (who succeded Aurangzeb as sovereign) recognized the claim of Hindus over the Gyanvapi property.

Yours is a philosophy that recognizes force theory of law whereby sovereign is the one that has force and can implement its commands. As per that view you say that one's valid ownership titles can be decimated and extinguished by the sovereign if the sovereign applies that force to implement its commands of destructing temple and then issuing a firman to incongruently install domes on top and to resist any attempts at (regaining back control of)* such forcible conversion of property - no matter what the principles of equity, justice and good conscience may lead one to. As per that view, you also say that Britishers did not recognize valid title - and so there's no valid title merely because British was a sovereign, without considering the principles of equity, justice and good conscience.

Non-recognition by a sovereign is no basis to rejecting ownership titles. An ownership title is vested by the dint of application of one's labour and not because of recognition by a sovereign or not. The labour has to be justly applied and not through application of force or through an act of theft. I am owner of a car I build because of the above principle - not because the sovereign recognized my ownership. Well, my view is again a philosophy that I subscribe to.

I can bet on my life that my philosophy is what will usher in world peace, and your philosophy will only result in creating a system which is wrested between sovereigns with waxing and waning amounts of force.

I'll also tell you what your line of thinking and what your philosophy entails - Nazism. As per Nazis, jews were sub-humans who had no right of existence. As per your philosophy, it was okay for Nazis to kill jews because the prevailing sovereign of that time did not recognize their right of existence. Congratulations - you just legitimized the holocaust and many others preceding it.

I'd shudder to think of the value systems you have been raised on.

There is a beautiful temple where I grew up, it is over 800 years old and from a cursory look of the architecture it was clear that the temple was not like others, later I came to know that it was built by converting/repurposing (depending on your view) a Buddhist stupa. Can the Buddhists reclaim this temple?

Ownership of land depends upon recognition from the sovereign. The sovereign has always had the power to acquire land or otherwise extinguish title to land. This is true even today as the State (i.e. sovereign) can acquire or extinguish title to land through its eminent domain powers. The only difference is that today the sovereign's powers are circumscribed by statutes and the Constitution (although it is pertinent to note that right to property is not a fundamental right in India and post-Independence the right to property has very much been treated as a second class right by the Indian State). However - and this is the crucial point - the limits on the sovereign's power today cannot be retrospectively applied to the past to invalidate legal (at the time) dispositions of land made by previous sovereigns.
I don't think you have though through the ramifications of the doctrine you are proposing. Under your doctrine, any and all dispositions of land made by past sovereigns can be challenged on the grounds of "justice, equity, and good conscience" (which btw is not a ground to challenge land acquisitions even under the current legal framework). This will upend all titles to property and will in all likelihood flood the Courts with a wave of litigation. Furthermore, your doctrine will have severe ramifications for current owners. Anybody can come and claim that the land I hold title over currently belonged to some ancestor of theirs and was appropriated by a past sovereign (Mughals, East India Company, British Crown) without following principles of justice, equity, good conscience and the land should therefore belong to them even though my family might have been occupying the land for generations. This doctrine will lead to chaos and confusion and cause immense hardship and injustice to current owners. Furthermore, the Supreme Court in the Ayodhya judgement has clearly rejected this doctrine.
Coming to your point about the Nazi comparisons, I am not advocating that the power of the sovereign to acquire property in present times be unchecked. I am saying that past dispositions of property by previous sovereigns cannot be overturned by applying the standards of today. Furthermore, there is a vast, vast gulf between destroying temples and committing genocide.