what about putting down either a plastic barrier, or heavy thick sheet mulch (cardboard with a lot of straw/leaves/lawn clippings/grass)? or both actually...with the plastic barrier it would be good to not just cover the bottom but even staple them to the bottom of the fence so the roots of the creeper cant cross over.

or just...make sure the plastic covers not just the bottom but put it in an L shape against the bottom of the fence and the dirt on top should hold it into place.

dig out the area up to the fence, cut out whatever roots are migrating to your side, and then put down plastic or thick layers of cardboard...with mulch/compost and then bag dirt(or screened soil, etc)on the top to cover the cardboard or plastic where the kiwis will go. you would want to add a lot of dirt/mulch/cardboard over the plastic for the kiwis.

thats what i would do anyway, actually i do have to do this in some spots...cause i have blackberries going crazy with their world domination plans all around me =)

ah eventually the bberries will keep growing in and all around the garden...but digging out the roots(impossible to get them all), and sheet mulch on top holds them back from an area for a few years...i figure the areas i put down plastic underneath the sheet mulch will have a lot longer before the bberries infiltrate...they grow under the plastic though and come out the other side...but ah...at least they are an abundant edible, with no input or fussing over they produce huge amounts of free fruit=)
the native bberries are actually pretty cool....but the are mixed in with the hymalayan.

you can use other stuff too...plastic is kinda...well has a heavy environmental toll to produce, etc, but i can find lots of scraps of free random plastic stuff.
and re use it as a barrier in some spots..... some people use salvaged stuff, whatever is on hand in your space...like old carpets, linoleum, random building scraps....hugelkulture, straw bales or other mulch to build up on top of the cardboard/plastic.... and possibly make a raised bed on top of that with just a bit of bag dirt/screened soil, other growing medium on the very top.

Milehighgirl, we have a fair amount of Virginia creeper and it does tend to grow. My wife controls how far it goes by clipping it back habitually, but otherwise letting it have its way. The mature wood roots wherever it grounds and ours doesn't seem to be overly aggressive underground. She tells me this one is at least 30 years old, and we've never had a real problem controlling it.

On the other hand, it is tough and hardy and survives mishandling, so you probably won't do any harm to your neighborly relationship by whacking away at it. I wouldn't spray any of the main plant, but the rootlings are asking for it, and I'd readily put a tiny spritz of glycosphate on young leaves as they appear - same as I do to the sprouts from our yellow rose when they appear in our neighbor's lawn. (Our neighbor is handicapped and my wife maintains her yard for her, so our situation is not exactly like yours.) That hasn't hurt the parent plant at all but does put the brakes on its colonizing efforts.

Good luck,

Mark

If time and money are not an issue,I would dig a 2 foot deep trench along the fence line and put down a 2 foot stainless steel sheet metal wall.At least you would never have to worry about root suckers come through again.

glenn