I have some that do very well. No disease issues and bloom well. For a tall variety phlox David is white. A little shorter phlox is Blue Paradise. Has been consistently nice. Shortest for me is the candy series. A little black spot in fist year. Healthy every year after. These are very nice phlox and a good garden size. They bloom early and until frost if dead headed. Many phlox have been removed from my garden because of mildew. These varieties have stood the test of time. Theres a couple more I'm trying but have not had them long enough to pass judgement.

For some reason, they liked to get powdery mildew, where I lived before. Now I'm closer to the beach, but maybe there is a bit more air movement and there isn't a swimming pool next door, either.
I've Eva Cullem, Blue Paradise, Red= Starfire(?) White , probably David and seedling from it that looks just like the lavender form of it. Orange Perfection, which I would not have purchased had I not seen it in person. But there is Dusterlohe, which goes by another American name, I've forgotten, or otherwise its sometimes just listed as 'Purple'' by inexpensive mail order. I really preferred Mt Fuji, or Fujiyama, to David. The flower heads were larger and had a yellowish eye. But in heavy rain, the panicles might flop, when in full bloom.
Blue Paradise is spectacular colors in the early morning and/or at sunset, welll at least shade in either start or end of the day, for better enjoyment,
Trying a new 'Tiara'or double white, but maybe due to being underfed (?), it had small flowers and wasn't double florets, in any case. Possibly too young, might be reason for that. Not sure.
But newer ones seemed to all have smaller flowers, and shorter. Not sure if they 'Volcano series, or what. Not certain how to avoid fungus, other than possibly divide the plants, for better circulation, or remove lower leaves and then don't place them as close to the edge of the border.

I love border phlox, especially when it is highly fragrant *and* mildew free. I know of three resources to find out more about which cultivars are likely to do well in hot, humid conditions:

1. Plant Delights Nursery. If they grow and sell it, it is likely to do well in hot, humid conditions without mildew.
2. Niche Gardens. The same comments above apply here, too.
3. Perennial Pleasures Nursery. Although located in northern Vermont, the owner is a phlox collector and has years of experience. She could probably recommend which of her plants are likely to do well in your conditions. Almost all of my phlox has come from this nursery. I highly recommend it!

Hope this helps,
Ispahan

Here is a link that might be useful: Perennial Pleasures Nursery