Why don't you just layer one in a pot or the ground hollie hock. Softwood cuttings are easy as well. Lots of lovely new growth there begging for propagation.
Layering works well with honeysuckles hollie - just like strawberries
That reminds me - did you take any strawberries with you to your new house? I can send you more if you want any.
Might be worth trying layering on the roof if you can get the pot secure.
I'd go with the cuttings, you never know when your neighbour might decide to hard prune the honeysuckle
Try everything, something will work. You can always take more cuttings when the growth is a bit less soft