It's not a tea, but have you considered using Ducher? Mine stay thick right down to the ground and are healthy and disease free with no spraying. I use my electric hedge trimmers on them and they come right back with a beautiful display of double white flowers.

I'm south of Sarasota and can suggest "Carnation" as a nice bushy rose bush with pretty deep pink flowers that bloom most of the year.

I got mine from Seminole Springs Farm in Eustis about 3 years ago and it is just about 4 to 4.5 feet tall. It might get a little taller but it's been moved twice (so far lol). Truly a carefree rose, doesn't need spray or much attention. Nice spicy tea scent.
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this photo taken a year ago from walkway below so the bush looks much taller. It has also filled in quite a bit since then :-)

Denise

I don't know how tall Angels Camp Tea from Vintage gets but it's a beautifully bushy rose with gorgeous, abundant flowers. I had to part with mine with great reluctance because the flowers faded too quickly in my hot garden. It was just about constantly in bloom with pretty pale pink flowers. A really great rose.

Ingrid

this may be a better photo to show scale with an indeterminate tomato on 8' pole on the left and 6' banana behind Carnation (before it got moved the 2nd time)
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Thanks for all of these suggestions! Imagardener, I had completely forgotten about Carnation! My mom has one- she just waters it (frequently with old rinse water from the laundry!) and throws old vegetable scraps underneath it and it is always beautiful! I am going to check out the other suggestions too, but sounds like these would fit the bill. Thanks all!

Tea is my favorite rose class.
If I had your landscape to work with, my first choice would be;
1. 'Mlle. Cecille Brunner', Because it was bred from a Tea rose parent, and shows all the important Tea rose characteristics, in my opinion it should be placed in the Tea class. I think the ARS does it a disservice by placing it with the Polyanthas, although it does bear smaller roses, c. 2 1/2 inches wide, I think it should be classed as a Tea because;

- of the Tea style of its bloom shape, much more exquisitly formed than the simple rounded shape of most Polyantha roses, though I'm also a big fan of that class of rose.
- beautiful foliage, each leaflet is a very dark green, almost a forest green, and there is a great abundance of it.
-smooth stemmed. Few prickles make it easy to trim.
-fragrant, a blend of old rose, with a hint of spicy black pepper.
Two forms of M.C.B would be good for hedging:
The original form grows to be a dense plant of 5' tall or just under, where I live in Northern California, because it naturally remains at c. 3 feet + a few inches wide, it would not need much trimming to keep it within a narrow bounds, because it is not very wide.
The spray version of M.C.B grows much larger and can cover an area of 8 feet in every direction. A plant near my home is grown as a hedge. It is kept at 6 feet tall by nearly as long and 3 feet wide to marvelous effect, but this would need regular trimming to keep it narrow. It blooms far more often than the climbing forms of M.C.B..released in the 1900's.
The blossoms of 'Mlle. Cecille Brunner' appear especially lovely when gathered in a 2 inch tall bud vase.
I would also try hedging these lovely Tea roses;
'Mrs. Dudley Cross' is a dense grower with few prickles and could be hedged, but because it is naturally a wide bush, would take more work to keep it a narrow hedge.
'Etoille de Lyon' which has been kept just under 6' tall, by 5 and 1/2 feet wide, here. Not many prickles. Light yellow roses have a delicious fragrance, like honeysuckle and cream to my nose.

What climbers are you considering?
Luxrosa

I can second the recommendation of Ducher. I live in hot, humid Louisiana and it thrives with no spray at all. I would also suggest Archduke Charles. AC is great because the flowers are different colors at different stages, which makes for nice contrast while in bloom. Ducher is a very full, lush bush with tons of blooms.

Thanks for all the input everyone- I will have to do some hard thinking on these! I like the idea of having a deeper/stronger color of flower against the butter yellow of the garage rather than a light color, although the lighter/paler colors are more my favorites. And as for chinas, I definitely will consider them too since they are healthy and floriferous.