Hi Rain,#
I know what you mean about the wild honeysuckles.
I haven't done it myself but I would treat it like a Clemenatis. I think they might root with the layering technique, but if that isn't practical maybe treat it as a Clemantis and take cuttings off the plant, use some root hormone and see if it works.
In my very limited and but ongoing knowledge about taking Clemantis cutting, Take a few inches off a stem so it resembles a T shape, then dip into rooting hormone, put in a large pot, keep out of a direct sunlight.