Your contention cannot be faulted. Indeed it is cul de sac.
The lines held by either side is too rigid to reason.
I find no solution in a hurry.
Personally, I would rather have a warmer relations with Pakistan even if the Kashmir issue hangs fire. It is not that I don't care, it is just that I see no solution and yet, on the other hand, I find no reason why one cannot be friends with Pakistan.
There is much that Pakistan can give to India and maybe if Pakistan wants, from India to Pakistan. For instance, Pakistan can give tourism, Pakistan agricultural produce including fruits, Muree beer, Shan masala, Sui gas, Calcutta's Kabuliwallhas from Kabul and NWFP (read Rabindranath Tagore's story 'Kabuliwallah' to realise the closeness of people and the pathos) and many other things of Pakistan. It will also lead to better and easier meetings of families divided by the Partition.
Why should one issue alone, where there seems to be no answer, wreck up the whole lot of common ground?