What to use for morning glory and Japanese honeysuckle?

I am doing weeding on The Bullock Track reserve at the eastern end of Western Spring. It is a neglected mess and Forest and Bird are trying control weeds there. I have been spending quit a bit of time there. Two biggest problems are morning glory and Japanese honeysuckle. Both run extensive runners along the ground rooting every foot or so.
Most roots are minor and just pull vine out until I come to more substantial root, normally where there is branching. These I cut, scrape and smear with paste. What would you recommend for that?

Aside:
Recently I moved to using Bamboo buster (BB) but the F&B are still supplying the “origina”l CutnPaste at their weeding days. (They got given some ). I have advised the organiser that they should probably switch to BB as we have woolly nightshade as well other usual suspects. I also wonder how old the stuff is. I could not find a DoM on the bottles — is there one I missed.

I also do work on a DoC managed Island where bottles were being refilled from a 5 litre pack. After one refill (MetGel) I realised that the bottle sloshed — the content was liquid, not gel 🙁 Ranger immediately put in an order for new supply. I have no idea how old that was..