Hello Klet. Bear with me, this will be a bit wordie and disjointed.
The Jackline is for only one purpose. It allows the Staysail to be lowered instantly WITHOUT changing the clew adjustment. If a person doesn’t mind dealing with the clew every time then the Jackline is not necessary.
The issue is this: the LP (luff perpendicular) of the sail is less than the foot length. That means that if you were to just release the halyard, the sail would not drop completely down. It would only drop about 1/2 the way down because the foot is still stretched out forcing the luff to tighten and stopping its movement toward the tack.
The Jackline allows the luff to move toward the clew, making its effective distance less than the foot and allowing the luff to come all the way down. It all works great when properly adjusted and is virtually never a problem.
About reefing the staysail: The Jackline has nothing to do with that. If you want to reef the staysail then you must modify it for that. You will need a number of things: a reef cringle on the luff. That is, a 2nd tack. A hook near the original tack to grab ahold of the reef tack. A cringle on the leech. That is, a 2nd clew.
About 4 reefing grommets spaced between the new cringles. When reefing you will need to release the halyard a few feet, release the clew, secure the new tack, secure the new clew, tie in the reef points, and rehoist the halyard. Easy Peazy.
In my case, I have no Jackline. I must readjust my clew every time I do anything with the staysail. I do have a reef. I have a large snap shackle that is secured to the turnbuckle. It “floats” on a short pendant that positions it at the right height to attach to the reef cringle on the luff. I untie my clew (the foot out haul) and retie to the new clew after lowering the sail a few feet. Typically, I will rehoist the sail before I tie in the reef lines.
My suggestion is: Keep the best of your staysails and keep the Jackline. You should not need to carry a spare. If you have any questions I will try again at articulating.
Good luck, Dave
JB reformatted per DK request.