The solution? Scotts 3 lbs. "Pure Premium" High Traffic grass seed mixture:
We hand-tilled the dirt pit of a backyard featured in the above video and planted the grass seed in early April. We got a lot of rain this spring and only one or two visits from Kira. (Note that we did not put down straw or enforce a stay-off rule, which were both recommended by most grass-growing resources.) A month or so later, we have a seriously lush grass-filled backyard. I have not taken a photo, so you will just have to imagine it for now. $27.29 (which includes shipping) for shiny, thick dog-proof grass! Amazing!