The trellis is 12 feet tall and 8 feet wide. In that case, while I have never gardened in your climate and I've never grown either of these roses, I suspect these two roses might be worth considering: Climbing Mrs. Herbert Stevens Climbing Lady Hillingdon Both are climbing sports of tea roses (NOT "hybrid tea" roses). I can't easily grow either of these in my climate north of Boston (with really rare exceptions the tea roses like more heat in the summer and winter than I can offer), but in your Houston area climate I won't be surprised to learn there are other rose growers here (perhaps on the "Antique Rose" forum) from the Houston area who are familiar with both of these roses, and can tell you better than I can whether they are climbing roses that do well in your area (as I suspect they might both be). You may well not find either available in a garden center, but you will find them available via mail order from rose specialty nurseries.

Going along with micahelg's statement, I am growing "America." It is a large flowered climber with high-centered blooms that resemble a hybrid tea. Unfortunately it is not cane hardy. It is too close to a shade tree, and only grows 5'. I wish I could see grow here in a sunny location. The flowers are coral colored and beautiful. I also grow Spectra, another large flowered climber, that I absolutely love. It too has high-centered hybrid tea style blooms. In France I believe it is regarded as a hybrid tea. Mine will reach seven feet tall. However, it is not a Zone 5-A rose bush. I have it in a very protected location that gets full sun but it protected from the wind. Although it gets cold temps, it would mimic a Zone 7 micro climate. The roses in this bed are tremendously vigorous. I also am growing what I believe is Dr. Huey (the common rootstock used for roses) and it puts on a tremendous display. It is a great climber and once was sold in commerce. It is cane hardy.

Crust_muffin, Cl Mme Caroline Testout has a gorgeous flower but sadly was a black spot magnet in my no-spray garden. Cl Pinkie took her place. Happily, she holds onto her leaves, has little if any BS and few if any prickles. She wants to grow horizontal but that's not her situation in my garden as you can see from the link below. She's only been in the ground a year. She has not been the massive bloomer after spring, but that may be due to her age. Maman Cochet, Climbing is a big Tea rose with gorgeous fat pink flowers. I don't know if she's flexible enough for your situation. (You do know - or maybe not - that climbing roses need to be trained at an angle or they will only bloom at the top rather than all along the cane due to apical dominance, so often you'll see them fanned out or running on a fence.) Here's a link to my blog about her. http://sherryocala.blogspot.com/2011/07/maman-cochet-climbing-first-two-years.html Another one that's nice and flexible is Reve d'Or. She's a pinkish apricot colored Noisette. She has thorns but not big ones like Maman Cochet. Here she is all trimmed up. If you want a once-bloomer, there's always R. Fortuniana. He has white double flowers in spring and will climb 25' easy into your trees. He does have small thorns but not bad. Duchesse d'Auerstadt is a strong yellow and not too thorny and is in between MC and RdO as far as flexibility. Rose Petals Nursery near Gainesville will ship or you can visit. I get most of my roses from Cydney now. She's sweetheart and can advise you, too. In fact, she came to my garden a couple of months ago for cuttings. Angel Gardens is in Alachua. Both have websites. These will take all the Florida sun you can give them. Sherry Here is a link that might be useful: Pinkie, Climbing

I doubt that any of the climbing Miniatures will prosper in that little sun. They may grow, but they won't rebloom well. This sounds like a site better suited to Clematis, perhaps?