The eruption that caused the year without summer had hundreds of times the explosive force of the entire Indian and Pakistani arsenal combined and threw almost 200 cubic kilometres of ash and tephra very high into the atmosphere. It was an event on an entirely different scale.
Saeculum
In the case of a limited exchange I'm quite sceptical of the study that suggested the ash would cause significant global cooling for a prolonged period of time (5 years+). I think they overestimate both the amount of ash and particulates generated and the amount of time it would remain in the upper atmosphere, alongside the extent of the resulting fires.
This is good advice, but I live near several major military installations and a major urban centre. My plan for this scenario is to bend over, place my head firmly between my legs and kiss my ass goodbye.
One Palestine is not a recipe for a stable state imo. You can deport the settlers back to their countries of origin, at least the European ones, but that still leaves a sizable contingent, something like two million IIRC people/descendents of people who migrated/were forced out of the neighbouring Arab states.
You have the Palestinian Arabs in Israel, a great number of whom have, at least to some degree, been complicit in the oppression of those in Gaza and the west bank. On top of that, they are considerably more materially wealthy and educated. Wealth redistribution could fix this, but would create resentment. Not doing so would create resentment on the other side.
You have a rift between the secular and non-secular populations, significant differences in beliefs and politics between the west bank and Gaza, you have secular socialists and zealous theocrats, all militarised (by necessity and justly, but militarised nonetheless).
A two state or three state solution is not just, but even with Israel destroyed, could a one-palestine survive even briefly?
No, I do get that, but the emissions from extensive fires across the region are still substantially different from what you'd see in the kind of event we have seen produce actual global cooling events like the 1815 eruption.
I'm willing to believe that it's possible, but I think the initial study suggesting it could happen makes some overly broad assumptions and I've seen subsequent studies fail to reach the same conclusion with similar analysis.