White clover does tend to spread a lot, so I don't think it would stay contained to the area where you want it.

If you don't mind having clover mixed in with the rest of your lawn, it might be a good choice (though it could take a couple years to get established).

If you prefer your lawn clover-free, then you may want to try a different route.

Before the wide-spread use of broad-leafed weed killers, lawn seed for use in the Northeast typically contained a fair amount of clover. It fixes nitrogen (reducing the need for fertilizer), does not grow above mowing height, and tends to stay green longer when we have our normal hot and dry summer days in July and August. It can actually be attractive mixed in with lawn grasses. But if you ever plan on using broad-leafed weed killers, you are then left with big patches of dead spots. And the modern preference for lawn appearance has shifted to all-grass (though this is probably not a healthy choice for the environment in most of the country, since it needs a large amount of water).

Hope this helps. We have a lot of slope to deal with too, and personally I have let the clover come in wherever it wants to grow. It does a fair job crowding out other, less-desirable weeds and the honey bees (the few that are left) like it. The oxalis, on the other hand......

I haven't tried it. A mix of deep-rooting, perennial, native grasses would be my preference or a native prairie/meadow mix. Whatever you use, you want plants that root deeply to hold the soil and plants that keep some above-ground cover all year to protect the slope from the falling rain. You can use an erosion control blanket or one of those smaller green, seed-starting blankets sold at home centers or maybe even burlap to hold the seed in place while it establishes.

What about some dwarf ornamental grasses for the top of the slope to control the erosion? Then, you can plant below that as you need to and time permits.

Good luck!

It just occurred to me that your slope might be receiving too much water from somewhere or receiving the water at too fast a velocity. It would help to find a way to mitigate this before you plant.