Probably now is a good time to transplant it. I wouldn't wait until summer. I'm not familiar with John Clayton Honeysuckle but if it's supposed to twine I've had luck using fishing line.

Howdy, Wolfe! Short answer: Yep. Longer answer: Use a soft, nonabrasive, stretchy material (old hose, bias tape, old t-shirt strips, etc.) to tie a figure 8 loop around the plant stem and the support. (loop around the stem, cross the ends, loop around the support, tie). Or use the fancy circular clips, or plastic "handcuffs for bags" or some other soft support. Now wait a minute, and you can resume twining on the new growth that shows up those 60 seconds. ;^D

Wow, sounds like you have your work cut out for you. With it so crowded and tangled, could you run something overhead so that once you got a stem free of the bunch, you drop a line down to it? I use 10' rebar wired together to make an arbor of sorts. Florida weave for the first 5' in height. Drop lines above that. Works for me. Its probably too late for you now but I'm using a straw mulching method this yr. that so far, has worked very well. At first I coughed on the price but in the big picture, has turned out to be very cheap. Rather than scattering the straw, it was laid down in blocks or flakes, a couple inches thick from the bale. Placed tightly to each other, covering everything except the spot for your plant where you leave that block out. I've read that some worry of suffocation but I've got some very robust plants that disagree :-) A benefit that I hadn't counted on, is that the mat is so sturdy once in place and watered in, there has been no time that I couldn't get in the garden, no matter how much rain. Kinda handy this yr. It doesn't blow away but I would think that in places of high fire risk, you might want to keep it a least suface moist for a while until it sets itself well to become a uniform mat. The first several trips tending the garden require more sure footedness than normal but the paths reveal themselves in short order. Good luck with your jungle.

I’ve never noticed that sort of die-back - but then we prune all the new whippy growth back fairly hard as soon as it appears in order to promote formation of flowering wood, and NEVER let root suckers grow - they are torn off (tearing them off helps remove the bud-wood they arise from...) as soon as they appear. I suspect that die-back might be due to the plant not being willing to expend the energy required to continue to elongate the unsupported growth. As for growing into a tree, my worry would be that it would become impossible to access any seed pods that form - they need removing to prevent the vine from seeding itself all around! The seed pods open explosively when the weather warms up in spring, firing the seeds quite a distance from the mother plant.....