Yes, wilderideas, clover works in Colorado alkaline clay. If you decide to go that route, white dutch clover would probably be the best choice. For best germination, you will need an inoculant to coat the seeds before planting. No biggy, it is just some fungus in a small packet with peat moss. Clover does need to be mowed. Consider that many consider it a weed. Your neighbors might not be happy if it flowers and blows into their yard. It is a legume which fixes nitrogen from the air into your soil. With the deep tap roots it will also go a long way to helping improve the clay and break it up. Another caveat about clover -- it stains clothes worse than grass -- just something to consider.
Take care,
jali