After some experimentation, I found that the simplest and most effective way to make WiFi-proof Photon applications is to leave everything in the default configuration and just enable the system thread:
SYSTEM_THREAD(ENABLED);
No mucking around with timers, countdowns, WiFi.on(), and so on.
This makes setup() and loop() run as soon as the power is connected—literally, even while the LED is still white—and keep running while the system thread looks for a WiFi, tries to get online, looks for the Particle servers, handshakes, etc.
Edit: the only exception seems to be if you need to register cloud variables or functions: in that case, you also need to set SYSTEM_MODE(SEMI_AUTOMATIC) and to register all the variables and functions before calling Particle.connect(). The docs explain this well.
Thanks a lot to the system engineers that worked on this feature. It’s awesome!