Reinforcing mesh that they use in concrete comes in a big sheet and is reasonably cheap. Hold it in place with the candytwist re-bar so it all matches then weave your honeysuckle into it. I use it to make rose arbours, fencing and trellis. It looks good rusty or you can paint it if you need to.
Honeysuckle is bombproof, have you ever tried to get rid of it? It keeps coming back if you leave a bit of root. So cutting it right back should not harm it, then do your trellis repairs, new growth will soon come back, but you could put a cheap montana clematis or passion flower in to bulk it up at first.