Unfortunately I don't have the time to read all the material on this thread, and my response is only limited to this important and interesting question stated in AM's post.
Two critical things:
1. India cannot negotiate anything with Pakistan under the threat of terrorism. The reason the diplomatic efforts with Musharraf were going well is because he was able to clamp down on the cross border terrorism after 2002 thereby giving the dialogue some credibility as being an effort made by the respective leaderships of two nation states motivated by national interest; as opposed to one where the main motivator is fear of terrorism/jihadi violence. Mind you, this isn't an India specific policy. No self respecting nation will allow terrorism to shape their policy for the obvious reasons.
The militancy supported by Pakistan has from its inception been an attempt to get India to the negotiating table, and India is aware of this. Therefore, movement towards resolution of Kashmir, especially in an environment like the one we have had in the past seven years or so with Pakistan sticking to its stated intent of not supporting cross border infiltration, would in fact continue to reduce the need for supporting those elements.
Furthermore, the reports being leaked right now suggest that the dialog with Pakistan had indeed progressed quite far, which also validates my point above, since your argument would preclude any such progress.
Historic Kashmir initiative stalled as Musharraf faltered
The argument of 'not negotiating under the threat of terrorism' is the non-sequitur here - the support for the freedom movement exists becasue of the Indian refusal to negotiate some resolution to the occupation, and the fact that the Indians have been negotiating despite the conditions on the ground, save for the cross border infiltration, indicates that your argument is moot.
2. National security always supersedes everything else. Even if a serving Pakistani leader is able to curb terrorism, the concern among the Indian security circles always remains... has the terrorism really been dismantled or merely suppressed for ad hoc purposes? Unfortunately the answer always seems to be the latter, and these concerns on the Indian side are always validated. The bottom line is that no country in its right mind will ever willingly open its borders to another state which has an effervescent terrorism problem akin to Pakistan's. And this is the basis of the world's common opinion, not some misplaced favoritism for India or a desire to target Pakistan, sure there will be the occasional comment against India for the sake of looking objective; but the bottom line is clear.
What you have to realize is that this "image" issue (a big obsession on Pakistani side) is actually a non sequitur. As long as Pakistan remains the hub of jihadi terrorism (a vetted fact) nobody will entertain bilateral arrangements which will put their own national security at critical risk, nor can you fault anyone for either outwardly or discreetly supporting this stance. I assure you the Western diplomats are well aware of this limitation.
This isn't about a 'serving Pakistani leader', the entire military and political leadership, except for the Islamist parties, was on board with the peace initiative. Your language implies another version of the oft repeated canard from the Indian side of 'who do we negotiate with' - negotiations on an issue of such import will not occur unless all power centers in Pakistan are on board.
Secondly, the 'adhoc dismantling' leads once again to the reson de etre for support of militancy by the Pakistani state in Kashmir as I explained above - the refusal of India to engage in a diplomatic resolution to the issue. Bilateral or any other engagement towards resolving Kashmri inherently addresses
the principal reason behind support for militancy, which makes your argument a non-issue. As I said above, my point is validated by the information being reported on the extent to which the Indo-Pak negotiations had advanced, despite no dismantling of the Kashmiri Freedom Movement on the Pakistani side, though Pakistan did keep to its word on clamping down on cross-border movement.
Now if your argument purports to explain why the Indians keep getting 'cold feet' on the issue, then I would argue that the Indian leadership shoudl have been upfront about these 'national security concerns' as you articulated, instead of going through what basically amounts to a charade of negotiations, only to step away at the last moment. It is a charade since the issues (of national security) you suggest are of concern to the GoI existed before the GoI entered into negotiations, and why go through the entire process and get so close to a resolution only to step back when these 'issues of national security' existed from the get go?
And this has happened twice now, at Agra and with the recent more detailed back channel diplomacy.
The other possibility to explain this backtracking is that your point about 'issues of national security' does not play into the situation at all, and is merely an excuse drummed up after the fact to explain away the failure to engage with sincerity.
Either way, it reflects poorly on the GoI's ability to engage comprehensively and sincerely with Pakistan. I might have bought your apologetics had the negotiations at Agra or in this particular case not advanced as far as they did, but the fact that on both occasions India and Pakistan were extremely close to a resolution only for the process to be shot down, by what I can only imagine is the iron grip of hardliners and extremists in India (possibly the military), gives lie to your argument of 'national security'. Were that the case, the initiation of negotiations themselves would have been subject to a concrete demonstration of Pakistani intent to the satisfaction of India.
This insincere behaviour by India is part of a pattern unfortunately - starting with the trilateral (British, Indian, Pakistani) acceptance of the condition of plebisicte in case of a disputed accession, to the agreement on holding a plebiscite under the UNSC resolutions, to Agra and this - at each step of the way the Indian leadership has been engaged politically by Pakistan, on the first two occasions come to concrete agreements, and then backed out. This pattern of deception needs to stop.