If you could post a photo of the bed and the wall, that might help. Meanwhile... here are some thoughts. You might try a heavier mulch like large pine nuggets. And instead of buying it in bags (which I assume you are) try to find a landscaping supplier that will sell it in bulk-- like by the truck load. (You'd need a pickup or a friend with a pickup.) This is usually much more cost effective.
I might change my mind on this after I'd seen what you're talking about, but I'd definitely at least begin to put in ground cover in specific places. Some to consider-- liriope (sp?) is grass-like, tough as nails, spreads pretty quickly without being too invasive (it usually fills in just where you want it to) and has pretty
flowers in mid summer. You might use this as an outside boarder to catch the run-off mulch.
Another that comes to mind is a very small sedum (anyone remember which I'm talking about?). It spreads very quickly, has beautiful little yellow
flowers in late
spring. It is invasive in the sense that it spreads so quickly, but it's super easy to remove. The nice thing about this is that it really perks up in the
spring-- rainy season-- but then sort of relaxes (regresses?) during the summer to a nice solid green mat. I've used this *instead of * mulch in many of my beds. Because it's a sedum, it really soaks up water when you'd need it to.