Jib hang ups are only a real problem in lighter air. It should just pop across with any load on it.

You should have the jib rigged low on the forestay adjuster. The jib clew blocks should touch the car when sheeted hard... if not, that could be part of the problem. You would be forcing the jib too high in the fore triangle. Lower means more room to tack through.

Be sure the jib luff is taunt. There should be NO load on the rigging "forestay". If the luff bows aft, the jib hangs up even more. The position of the "forestay" in the adjuster is irrevelant. Just be sure the wire is VERY loose when sailing. We generally have 1 foot or more of slack. That is where the bunjee comes in, It can pull out the slack, but not take any rig load.

Shorten the jib battens. They should just barely stick out of the pockets.

Tape over the batten ends. Start on the side of the jib and back over the end of the batten and to the other side. This can help prevent actual hang ups.

Tie the main halyard aft too. I pull the halyard aft then around behind the shrouds then back and hook under the downhaul cleat... and finally tie off on the halyard cleat. Be sure there is a moderate amount of tension on the halyard so it doesn't droop as the mast bends.

Don't just yank the jib through. In light air, I grab the bottom batten and shove forward which bends the jib and then pull through.