Fairway and Ephraim are improved varieties of crested wheatgrass. Crested wheatgrass is not native to North America, but is well adapted to the the arid/semi arid areas of the intermountain west. Crested wheatgrass comes from Siberia originally and was introduced to North America in the early 20th century. Older varieties are bunch grasses, but improved varieties such as Fairway and Ephraim spread by rhizomes (although you may need to water a little to get the spreading to occur)

Western and Streambank wheatgrass are native to the area and both are rhizomatous.

Western wheatgrass is more difficult to establish and looks less like a lawn grass than the other options because it is almost blue in color and has slightly wider blades. The advantage it has is that it develops really deep roots and stays green much longer.

Crested wheatgrass is probably the fastest and easiest to establish and streambank wheatgrass falls somewhere between the other two.

If it's going to be a play area for kids, I'd be a little wary of clover for two reasons. For one thing, it will attract bees. For another, it can stain clothes. If you decide to use it, you may want to use Palestine strawberry clover. Strawberry clover is similar to Dutch White clover in appearance and growth (the flowers have a slight strawberry shade to them). It does better in alkaline soils than DWC, but isn't as drought tolerant (but Palestine is the most drought tolerant of the strawberry clovers).

I wouldn't till, especially on the slope, where it may cause erosion. If you can water to establish the seed, you could plant right after the heat breaks. Depending on your first frost, that may be pushing it for the western wheatgrass, but the crested and streambank germinate faster. I'd water for three weeks (adjusting for rain) even if you see germination before that. You'll want to try to keep the surface moist the whole time if possible.

One option might be to get a little crested and streambank wheatgrass down to hold the soil in place, then do a dormant seeding with all three. Or you may opt to skip the western wheatgrass altogether. The crested and streambank wheatgrass probably look more like traditional lawn grasses than the western wheatgrass does.

If your precipitation patterns are like ours (and it sounds like they are), if you don't water at all, your lawn will likely go domrant in mid to late July and spring back in September. Last year, I watered three times. So far this year, I've watered once. I'll probably water again toward the end of July (unless we get some rain before then) and then once in August. My lawn stays mostly green if I water it three times a summer. I'm hoping that as the grass matures, I may be able to cut back to two times a summer, but that may be wishful thinking.

Once you get these grasses established, you'll want to make sure you don't overwater them. You don't have to get as extreme as I have with water, but I wouldn't water more than every other week or they'll probably suffer and maybe even die. They can withstand the spring and fall water they'll get from nature, but really do best when they don't get too much.