I suggest you re-post in the main forum in order to get some traffic on your question.

I wouldn't mind having a better look at that wall before suggesting something with a lot of root mass, like daylilies or shrubs. There is not much lean on that wall and pressure from within is the last thing you want. I've been poking around my rock walls and garden lately and have noted how much root mass is tending to migrate to areas of consistent dampness. For example, I have a pot standing next to a plant that has a bulky root mass, and although the plant can grow best where there is light, the woody base has pushed itself under the pot. Quite intriguing. In your situation, this tendency is aggravated by the downhill slope, which is where water, and thus roots, will go. Therefore a plant that spreads by stolons would probably not grow uphill, but you may not want to risk it - so none of your Houttuynias or St. John's wort, for example. Something that mats, in contrast, could easily by mowed by the neighbour (or their mowing people). A couple of matting plants that I have had good success with are a spreading veronica (note to self and others: do NOT google "spreading veronica") and a matting dianthus with bright pink flowers. Not sure how they would handle full sun in your climate, but the moisture retention of the rock would help. I think the thymes would be OK too. Which way they spread would partly be determined by the sun - they would grow primarily toward it. I agree that the sedums are not as weed-suppressing as you might think. One that might be would be Sedum 'Angelique', and there are others. Sedum acre would probably also work - but as Yardvaark's description of how to root it suggests, it is rather easy to propagate and so your neighbour's mowing might get it all over her yard - so easy to miss a bit that falls. 'Angelique' will also root where it drops, but because it's bigger and not as fragile it is easier to control the bits. All ground covers need periodic haircuts to avoid getting leggy, woody, and sparse. KarinL

Kimmiek: I have similar situation.I did have ivy there and I was covering sort of ok, but it was getting quite big touching my windows and my windows were always wet.Needs lots of training also.I cut it all off this Spring because the water it accumulated was always touching my windows and the paint was peeling off.So I have seen a similar fence and it was kind of landscaping fabric green in color made of plastic like material .This fabric covered the fence nicely and all you could see was lovely green color.No maintaince and no problem.Its been in our neighbourhood fence for about 3 years and always looks clean and green.So this is what I intend to do with mine.If you want more info I will have it as I have to do mine so I will find out exactly what it is.It has very tiny wholes in it like ventilation wholes, but gives total privacy and looks great.

I'd look at passionflower (Passiflora sp.) or star jasmine, Trachelospermum jasminoides. Both are evergreen and rather dense vines (star jasmine sometimes trimmed as shrubby hedge or even groundcover) and should provide good cover. For a 30' hedge, I would pick one or the other but plant them in multiples for the fastest coverage. Vines always want to grow up but if you start early, you can train them to spread sideways as well as vertically.