I live in way way upstate NY. First I'm assuming that you do not want to go through the trouble of digging them up and freezing them for 6 weeks. That would be the best way to have any Lily you want. They need to be covered when frozen. But thats not what you want right?
Any hardy winter bulb, INCLUDING LILIES needs to be frozen to grow well. Some can handle the high 28-32 temps as enough cold. Usually in area like yours it doesn't stay cold long enough. One would think none will do well there if not frozen in ground for 6 weeks. But there is the good news that Lilies are extremely forgiving bulbs. They can take a lot of abuse and still grow fine. Winter hardy bulbs are not harmed by the cold. Either 28 or minus 60. I've left Lily bulbs on top of the gound under the snow and they grow fine. The ONLY reason hardy bulbs like Lily, tulip, daffs are planted 6 inches deep is to protect them from the HEAT not the cold. I suspect you need to plant them deeper than you are. 5 inches is perfect here. In texas I'd guess 6 inches deep plus 2-3 inches of mulch. They are getting too hot.
Also, since they are getting too hot don't over water them. they will get boiled to death. I recommend you try the same varieties planted deeper with 2-3 inches of Cedar mulch. Let the rain water them not you. They can handle dry periods. I NEVER water my flower gardens.
Suggestions that should work well in TX....NEGRE--a very dark red upright bloom.......NIPPON- 9-10 inch bloom of white,pink yellow blush with a dark red edge. Only availible at "dutch gardens" I think.....Tom Pouce- side facing, 6", pink & yellowish blend.....REGALE- a purple longeflorum easter lily.
Have a good day

I am growing Casa Blanca beautifully here in the middle of Houston. I ordered them from The Lily Garden. I do not dig or freeze or give them any special treatment. Except to pick off the snails, of course! : )

Hopefully some other hot weather gardeners will have more suggestions for you (and me - I love lilies!)

Hi Joe,

The two lilies you already have, Longiflorum and Formosanum, are the most heat tolerant of the lilies - so no help there. :)

"lilium guy"'s suggestion to plant deep and mulch is a good one. In addition you might want to add companion plants that will keep the ground shaded around the bulbs. As the saying goes, lilies like to have their "feet in the shade and head in the sun". That said, lilies are fine with part sun - and in your case morning sun would probably be the best.

-Helen

Hi again Joe,

Another good heat tolerant lily is the Madonna Lily, L. Candidum. "Cascade" is a better strain of it. It's cultivation is different from other lilies. It needs to be planted shallowly because it puts up a rosette of leaves in the Fall that overwinter. The flower stalk energes from this rosette in the spring. It also needs basic pH with good drainage conditions. It blooms late spring/early summer and then goes dormant through the rest of the summer.

I have some I grew from seed that just bloomed this year. They are beautiful and have a heavenly scent.

Candidum is resistant to virus and so can be a virus carrier. Growing them from seed ensures that no virus is transmitted - but you have to wait a couple years to get blooms.

"Buggy Crazy" sells both bulbs and seed of Lilium Candidum. Since she grows her own bulbs (vs. being a reseller) she would be a good bet for getting a healthy bulb.

http://buggycrazy.vstore.ca/

Hope this helps.

-Helen