You could try Old Garden Roses, also called Antique Roses. Because they are disease resistant, they DON'T HAVE TO BE SPRAYED. I have grown many Old Garden Roses in my home in New Orleans: my front yard was very open and faced WEST, so it got that laser-cannon hot afternoon heat. The roses just laughed and flourished.
Certain types do better than others. I had China roses, Tea roses (note this is NOT "Hyrbid Tea" rose), multiflora and Hybrid musk. They all did great. The specific name of ones that I had were Prosperity, Buff Beauty, Archduke Charles, Hermosa, Perle d'Or, The Green Rose. I now live in Covington, (my house faces SOUTH) and roses I've had here include Reve d'Or, Crepuscule, Souvenir de St. Anne, Climbing Old Blush and Mutabilis.
One word: it's hard to find any white roses that look good down here. Every one I've tried does nicely in cool weather but the blooms look shabby in the heat.
I got all my roses from the Antique Rose Emporium for 2 reasons. 1) They are in Brenham, Texas, so I KNOW if the roses grow well in their heat, they'll do well for us. 2) They sell only "own root" roses- none are grafted.
Good luck, whatever you decide!

You could try Old Garden Roses, also called Antique Roses. Because they are disease resistant, they DON'T HAVE TO BE SPRAYED. I have grown many Old Garden Roses in my home in New Orleans: my front yard was very open and faced WEST, so it got that laser-cannon hot afternoon heat. The roses just laughed and flourished.
Certain types do better than others. I had China roses, Tea roses (note this is NOT "Hyrbid Tea" rose), multiflora and Hybrid musk. They all did great. The specific name of ones that I had were Prosperity, Buff Beauty, Archduke Charles, Hermosa, Perle d'Or, The Green Rose. I now live in Covington, (my house faces SOUTH) and roses I've had here include Reve d'Or, Crepuscule, Souvenir de St. Anne, Climbing Old Blush and Mutabilis.
One word: it's hard to find any white roses that look good down here. Every one I've tried does nicely in cool weather but the blooms look shabby in the heat.
I got all my roses from the Antique Rose Emporium for 2 reasons. 1) They are in Brenham, Texas, so I KNOW if the roses grow well in their heat, they'll do well for us. 2) They sell only "own root" roses- none are grafted.
Good luck, whatever you decide!

Ligustrum.

I have grown Encores for more than ten years in full sun here. I am surprised you had trouble with them, although they are not my favorite shrubs overall. (I am assuming that you watered them regularly their first year. If not, that's the problem.)

I am a huge fan of Indian Hawthornes. They need trimming no more than once a year to maintain the size you want indefinitely, and they are impervious to heat, drought, disease (white ones. Pinks are a different story.) and insects. If something does well for you, plant more!

I am also surprised that you lost Loropetalums. I have grown them for more than 20 years at my house and at my church. Once they get through their first full year, they are as drought tolerant and sun tolerant as any plant I can imagine. Did you do a good job of soil prep in the beginning? Even a good wide hole will usually be all they need, as long as you water regularly the first year.

Some others that I can recommend: Shishi gashira camellias, hollies, abelias, spireas, boxwood, crape myrtles (there are dwarfs), and although they are not shrubs, they have the presence of shrubs, grasses. I grow three varieties of Miscanthus plus purple muhly. All are dead easy. The muhlys are my favorite because they are small, their foliage is very fine and they are showstoppers when they bloom.