I would say a combination of 'yellow archangel' (also called false lamium, and sometimes goutweed, though 'archangel' is what it's listed as in the hortiplex here) and crown vetch would be your best bet...liberally studded with yucca plants, if you can find a nice strong back to put them in place. they don't seem to mind clay soil as long as it's on a slope...

I'm a pennsy native, and the combination of slope and shale is daunting- my parents added the third S- shade. the archangel is the ONLY think that grows on their property besides mayapples...but I got my original plugs from a lady who had it in full sun as a groundcover for when the deer ate everything else.

groundcover roses, lavendar and artemesia also make good second-string choices, once the others have established themselves...

and I wouldn't worry about the weeds too much- my mom got over them when she retired, and just has me scythe things off at knee height round about july (going over there this weekend, the rain's been helping things along)

wish I were closer (I'm out on the delaware) I'd come give you a hand!