Mike, the long term solution to slow, efficient watering is micro-irrigation. Lowe's and HD both sell it, and probably have classes to teach you how to do it. It's easy, cheap and fun.
Here in Sarasota, we have had once a week watering restriction in place since before we moved here, 12 years ago. But there is no restriction on using micro-irrigation except that no watering at all is allowed between 8am and 6pm. It keeps the water close to the ground, so very little is wasted to evaporation by spraying up into the air, and also is low volume application allowing it to soak in well.
Your mulch will definitely help with water retention and weed control in the long run, so hang in there with that. I agree with everyone else on the landscape fabric. We have it under gravel pathways and driveways here, but that's it.
