Hi Bridget, you can control Japanese honeysuckle effectively in that habitat using a two phased approach. The first step is cutting all the stems at about waist height, and the best tool for the job is a petrol powered hedge trimmer. If you don't have access to one it is a much bigger job to hand cut the stems. The hedge trimmer is fast and effective. You need to cut all stems to make sure all the vine in the canopy dies. Phase two is spraying the remaining vine at ground level. Glyphosate works well for this, and is unlikely to impact on the kahikatea provided you don't spray the trees directly. You will need to follow up spray several times, possibly over a few years. Eradication is really difficult, but you can effectively control the infestation and minimise its impacts on your kahikatea stand using this method. Best of luck, Tom.