Thanks, everyone. I'll try an Engenius outdoor AP and see how it goes.
One more question: is it possible to set it up to share an SSID with my two routers, so that the network is seamless and devices just choose the strongest signal, or does it need to have a unique SSID?
Thanks for the idea, but there's only our bedroom window and a sliding glass door on that side of the house and my wife doesn't want electronics up against either one. And once you move the device away from the window, the stucco kills the signal.
I could use some advice on the best way to get wifi out of my Faraday cage of a stucco house. I'm not opposed to spending money and/or replacing my current routers if it will get me a better overall setup, so don't feel constrained in what advice you offer. Here's a diagram of my current...