From what I can understand, the unrest only happens in Kashmir Valley, the Muslim majority area. Ladakh is also Muslim majority but not to the same extent as KV, and the Ladakhis are also a completely different ethnic group and want nothing to do with Kashmiris.
This would be a final solution to be honest, no sane person could object to this, India has to spend a lot of money policing people that don't want them there and giving this region to Pakistan would solve most issues.
You are partly right in that the resistance mostly happens in the KV, but it also happens in other parts where there is a large Kashmiri Muslim presence, that includes parts of Jammu, and the Kargil region which is part of Ladakh, but to a lesser degree than the KV.
There would be no need for a large military presence in Jammu areas and Ladakh areas if nothing at all was happening there.
Jammu also had a Muslim majority till 1947, when there was an organised Muslim genocide, which resulted in around 200,000 people being killed, and a larger number forcibly expelled.
As I mentioned before, your idea has merit, especially if it means the killings stop.