Except for the issue with the drainage, the creeping thyme sounds like a great idea. It will certainly be able to handle the summer heat, is quite drought tolerant once established, low enough that wind is not a factor and can tolerate some pretty cold temperatures as well. And it will stand up to foot traffic.

Drainage is relatively critical with most plants - there is a short list of those that will tolerate less than ideal drainage, but for the most part, drought tolerant groundcovers require good drainage. What is there about your new garden that leads you to believe drainage is poor and what can you do to correct it? FWIW, any soil improvement you can do now before major planting will benefit you and the garden in the long run. I typically suggest to my clients to take the time and invest sufficient dollars into improving their soils before spending a lot of money on plants which may fail because of poor growing conditions.

My first question would be: "what grows wild in that area?"

Of what grows there, is there anything you would want to plant in your yard as a ground cover?

Have you considered sedum? There are many varieties, and they put up with a lot of neglect and abuse.