Hey ted,
I'm sure this is way too late for you to respond, but maybe it will help someone. So I'm working on a similar task, and I have found that it's pretty tough to use the esp8266 for wifi direct.
The reason being that it's a complex protocol that (I was told, not sure if this is true) requires an operating system and multiple threads, and since none of the embedded operating systems have direct support for wifi p2p, you would be implementing a lot of the protocol entirely from scratch. That's certainly possible, but I opted to switch out my esp8266 for a raspberry pi zero which is about the same size and runs linux which has a little better support for wifi p2p. I bought a usb wifi card , specifically the edimax7811un and I soldered it to the board. I then had a bit of a tough time installing drivers, but once I got that done, there is a nice github repo that has a wifi direct test app to help make sure everything is working. I have a bunch of relevant links, but it's late rn so I'll find them all tomorrow and respond to this post