I think a root barrier maybe the only answer. Not all neighbours can be bothered to resolve problems they are causing, if it costs them time or money!
We get bindweed under the fence from one neighbour & ground elder & bamboo from the other!
We have twice tried emptying the borders, digging every trace of root (or so we thought) out before replanting. Pointless, as others have said. Loads of the weeds still pop up & more grows under.
The funny thing is both sides have well manicured looking gardens with paid gardeners, who obvioulsy only tend the front of the border & what goes on at the back or behind the shrubs gets ignored!
I get so fed up with glyphosate looking like it hasn't worked, or it raining, or being too windy to apply, it needing to dry before the dog can go out... I now just tend to pull them out when I see them.
It seems so unjust that we will probably end up putting root barriers along all the fences both sides at our expense when they should be our neighbours problems, but that's life.
Or back to the glyphosate. Beware of strengthening the concentrate, that can apparently just kill the plant before it has time to take it all the way down to the roots, so is counterproductive.