Create a connection with the web socket server after connecting to wifi and rebooting with load()

Actually, that's not quite right, after looking at your code file, you've got the module in your code and it would appear the Espruino Wifi Manager (I'm assuming the code belongs to that) checks the validity of the network credentials supplied by first test connecting to the Wifi network before writing to flash & rebooting (nice!) so if you bring your websocket code into there, below this line in the start_wifi function:

  console.log("Connected to: " + wifi.getIP().ip);

and defer calling load() until the websocket sends the credentials (your test object) that should work.

Given this would seem to be a one way, one time exchange of data, you could probably simplify your code again by making a HTTP POST with the data, and have a backend which can handle forms (assuming that's possible).