I have a hybrid Phlox called 'Wanda' that is amazing. It is a pink variety, but would perform even better than 'Minnie Pearl.' It blooms continuously. This is such an awesome plant. I have rooted it in a glass of water. It even blooms while it's rooting! I have included a photo with info about it. Out of all the Phlox plants, this is the one I would bet money on to do well for you.
I also have good luck with 'Shockwave.' It blooms once, but the foliage is beautiful. I've had this one for three years. It's good.