There are some ground hugging Cotoneasters that would carpet this slope very nicely. We have one that is dead flat to the ground but, unfortunately, I don't know its name.

BA could you mean cotoneaster dammeri' evergreen and ground huging,

C. dammeri is the closest name I have seen, Cliffo, thanks for that. I have just been web browsing this and would say that ours is, if anything, even tighter and more prostrate! None of the pictures I have seen show a large enough area of the plant to be sure. I will have to put my own picture up and see if anyone has ideas.

Carnea spreads quite quickly too it also it produces a yellow flower

Then there are the prostrate conifers.

there is also a prostrate salix - I 'think' it is repens which hugs the ground and has lovely little catkins. We've got one in the garden but the label disappeared years ago... It spreads to such an extent that we have to prune regularly - so would be perfect for your bank.

Cotoneaster 'Queen of Carpets' - spreads for miles, only gets 1/2 inches high. Only trouble is, you've got a membrane down, which will prevent it spreading sideways and also rooting as it goes. And Bulbaholic, that might well be the one you've got.
As you've got the membrane down already, how about putting things like Saponaria ocymoides, Alyssums, Aubretia, Arabis, Iberis - these are all spring flowering, admittedly, but they have something in common - they all grow from one central point and the topgrowth spreads out all around that central point, doesn't need to root.

You're right Bamboo the cotoneaster and salix want to root as they go. Whichever cotoneaster we have is right across a path and regularly gets walked on