I meant to mention that I'm in Oklahoma City, zone 7a, and the raised brick bed gets morning-midday full sun.

That is a tall order. I like the creeping junipers too, but they are the opposite of fast growers and a three-feet cascade would be a long time coming, if ever. If the damage is just along the top, it could work but again, it won't be fast. I would go for an ivy like Hedera helix. It won't be invasive in your zone, I don't think, but it won't be invasive in your application, period, because it will never set seed.

I would not plant ivy if i were given it! You will not be able to get rid of it once you have it, not to mention it is ugly!

what about wintercreeper or creeping phlox? two completely different looks to choose from.