Creeping thyme and woolly thyme
Crown vetch (although I think some consider this a weed. According to the Jung's seed catalog "once established, grows so thick it will choke out most weeds."
Sweet woodruff
vinca
Veronica
Ajuga
Bishop's weed (although, like vetch, I think this can be invasive)
Check out High Country Gardens for more ground cover ideas that are xeric. There are also no mow grasses.

cheers,
Norabelle

Here is a link that might be useful: High Country Gardens

If it's as bad as it sounds, I don't blame you about the danger of mowing. I'd want more perennials, but doesn't sound too practical there as you need things that will smother weeds and don't want to have to prowl through anything that big to do it yourself.

A couple smallish trees and shrubs might work in there to break it up. Hope it is all enough to help with erosion. Grass doesn't root deeply enough for that, and I've seen what might possibly happen.

Sounds too involved to terrace, but that is an option. Then you could have fruit trees, berries, all sorts of things and be able to access them more easily. Can't help thinking of a few redbuds and dwarf fruit trees, daylilies and naturalized bulbs for spring.

You could always direct sow a few hardy perennials among your ground covers. I like all the ideas that were posted already. I would highly recomment throwing some black eyed susans in there for a bit of a break from the ground cover. They do well in tough areas and would look good with almost anything.

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We had a problem hill, too. I ended up planting rudbeckias, comfrey, artemisia, coneflowers, phlox, monkshood, daisies, perennial pea, angelica & tiger lilies (wild asters & goldenrod showed up)(jacob's ladder, creeping sedum & lady's mantle have gotten lost on lower edge). It has filled in these past 2 years & I kind of like it now!

This sounds like my back hill. My all time favorite for the shady part of the hill is lamiastrum / commonly called archangel. It covers well, with deep green and silver variagated foliage. In spring it has yellow flowers. In another part of the yard we have small generic daffodills which pop up through it. Lamiastrum is vigorous but it seems as though that's what you want on the steep hill. In
our situation, wild violets, forget-me-nots, and some other
things have arrived. ajuga, waldensia (false strawberry)

On the sunny part of the hill, I'm working on sort of diagonal spreads of purple coneflower, black-eyed Susans'
gooseneck lysimachia, ox-eye daisy,gold plate yarrow, sweet rocket, and we have several large clumps of ornamental grasses.

Our hill is quite big and it's a 6 year project so far but
each year is better and we do have memories of when it was covered with nettles, Japanese honeysuckle, thistles, Tree of Heaven, etc. etc.

Chris