er...20 minutes 4 days a week? Unless your system is less than a trickle, I think you'll be drowning those poor daylilies. Maybe you have a different variety than the ones we have out here in CA, but ours only need to be watered 2" twice a week.
You never get less than 2" of rain a month in Lousville, according to the averages mentioned on
www.weather.com. May looks like your wettest month on average with 5". In LA, we're lucky if we get 0.5" of rain. I'm jealous of Kentucky! (never thought i'd say that)
Looking at the water requirements for the plants you specified:
Boxwood - hearty. These plants prefer partial shade, but they do all right in the sun. It has shallow roots and will do poorly when exposed to long periods of dryness.
Ajuga - which one? Ajuga Reptans is a ground cover. Ajuga Genevensis has blue, rose, or white flower spikes, and tolerates more sun than its brothers. Ajuga Pyramidalis has blue flowers with purple bracts that press up against the flower. Each of these have different preferred growing conditions and water requirements, but in all of them, look out for root rot caused by fungus and nematodes (microscopic worms), which can be encouraged by over-watering.
Monkey Grass - haven't ever seen this in person, but sounds beautiful, apparently it's a staple ground cover of the South. Do yours have the little white-lilac flowers that are supposed to hide among the blades of grass? or are the blades veriegated with white stripes? Do they tend to grow in clumps, or diaganally run? Anyhew, there are so many different types, but all are drought tolerant, invasive, and love well-draining soil (the clumping varieties do ok moist, non-draining in soil even though they do better otherwise).
Hostas - should be in full shade. these do well in a bog, why are they in your sunny front yard? Are they really doing well?
Is your neighbors' landscaping similar to your own? Let me know, this is fascinating.