Not a bad list of options Sakura, but they will not be met in-game. Not because CCP will never let them due to game-mechanics (though this is ofc the nr1 reason atm) but because there are several factors in the way of your ideas here.
1. Luminaire as a DMZ will have to be agreed on by the entire Federal population of the system for the governments to agree on pushing it as an option and then bringing it up to the Senate and then becoming reality. They are extremely unlikely to like the idea, but it's not impossible.
2. So far it seems Sansha's nation has not been enough to form a mutual pact. The war still rages on despite the incursions. Ofc this is, again, game-mechanics' fault. Incursions will have to be evolved into something else, something far worse for the outsider enemy idea to kick in. That or the other pirate factions or even a whole new danger starts working up. Another small, but possible fix.
3. Given combined history, the only 'secure path' the Fed will ever likely agree with is using the existing gates as a highway-to-Luminaire from the State's border overseen by Fed-navy ships and constantly patrolled, with heavy limits to how many and what kind of ships get to move about at a time. This might be agreeable to both sides, but it will require lots and lots of trust that is not likely to exist atm. Another possible future option, though.
4. This one will never happen. It simply won't. The Fed prides itself on having a powerful and integral trade network that spans the whole Fed and keeps the economy on the level of being the de-facto most powerful one in the cluster. Becoming dependent on another faction for their economy to run is never going to happen, it will never be accepted, much like the State won't accept not having Caldari Prime. Worse is, it's not just trade. The Fed prides itself on being 100% independent on everything, end of story. I foresee no way this will change unless CCP retcons the Fed into something entirely different than what they are.
Also, note that the State is not the 'government of the Caldari people' they are the government of all the Caldari of the State, and that's it. I don't know how many percentages of the total Caldari population resides in the State but it is by far not all of them, a great deal of Caldari still reside in the Fed and a huge number of those live on Caldari Prime. The Caldari Prime situation is effectively a great deal of Federal Caldari (among other people) occupied by a non-Federal power who happen to be Caldari as well. The State may claim that they are the only real representatives of the entire race, but this claim is not even remotely true, no matter how hard the State's people wish it was true.
Thus technically from the Fed perspective Caldari Prime as a planet were under the control of "The Caldari" to begin with, as in it was the lawfully owned land of all the various Caldari Nations on the planet and everyone else who live there. Saying to the State that they may have the planet is likely going to be completely unacceptable because that's legitimizing the hostile take-over of Federation member-Nation's land - as a huge alliance, it's not a good idea to out-right ignore the practical theft of alliance members' property, it defeats the point of having the alliance in the first place.
It might be possible for CCP to create a situation where the State and Federation co-exists and the State get's the property they effectively abandoned a long time ago back, but it will require a long time of careful and slow dealings to get us through this highly complicated situation and to that point, without effectively displaying the Fed as utterly weak-sauce pushovers who will cave in on their own principles whenever convenient to them, but hey, not like the Fed has not got a good wack if the incompetent stick before...