Hello New Mexico,
If you are concerned about roots in the ground, then have you considered container planting using trellises to grow vines and create the height for shade?
For instance, scarlet honeysuckle (Lonicera sempervirens) will grow about 10 ft. per season. It will take full sun to light shade in any soil. It is beautiful and drought tolerant as well.
I thought of this vine when I realized where you are located.
Another suggestion would be to create several sky gardens. This was popular back in the mid-70's when I was growing up and I haven't seen it anywhere since then. But it was very pleasing to the eye and created shade with out digging up the ground.
It would help to see pictures of your yard if you have any.
Hope this spurs your imagination forward a little.
Good luck

What is a sky garden?

Simply put, a sky garden is a wooden tree-like form with hanging wood planters. It can be made portable so you can move it around, or it can be a permanant fixture by anchoring the 4x4 post into the ground. I'm sorry I don't have any pictures that would help you to see what I'm describing.
What I thought was particularly nice about it was the fact that you could make it in what ever height you choose. Some of the nicest ones I remember had vines growing up the post. I suppose that was pretty inconsiderate of me not to describe this in my last post. What was I thinking? lol

Thank you for your help.

Native American Seeds, www.seedsource.com, has a grass/forb seed mix especially formulated to grow on septic fields.

Around here, alot of people just plant cannas on & near their leach fields.

Cannas would probably go nuts with all that sunshine and steady moisture. And what a show! (I'm thinking 'Tropicana' and 'King Humbert' but that's because I only know a few (I'm envious of you year-round canna growers; we have to lift 'em here)... More here...

Here is a link that might be useful: Cannas

i have a leach field with shallow perforated pipes. i would like to plan ornamental grasses. would they be too invasive? thanks very much. sherry

As the owner of a company that Specializes in these types of septic systems I can tell you to plant NOTHING!!!! Roots will clog the perferated pipe. Your system will suffer and the repairs will be expensive and every thing you planted will have to be dug up.