Here's another possibility- If the battery was getting pulled down by load that was on it, shifting to neutral, or just shifting for that matter may have pulled the voltage down enough -briefly- to cause a partial shift, and stall the engine due to fuel cut-off. If the shift mechanism doesn't cycle completely, the engine may not start again until the key is cycled, or it is shifted to neutral again causing the shift cycle to complete. I've noticed that the shift actuator actually draws quite a bit of power during shifts. I notice it when my air compressor is running and I shift- the compressor slows down noticeably. I have had it stall if I try to shift directly into 2nd without moving, at idle, particularly if it's cold. I once had to 'rock' the machine a little because the shifter was 'hung' and couldn't move, which also caused the display to start flashing. I turned off the key, turned it back on, rocked the machine a little, actually heard the shifter finish it's cycle, and no more problems. There is a voltage threshold for all computer controlled engines where engine may still crank but not start- don't know how sensitive the Honda's are, but just because it cranks, don't mean the computer will actually fire the injectors, or ignition. Just like bad grounds, low voltage will cause crazy s**t! Piston Honda may have nailed it- the brief rest may have allowed the battery to recover just enough to break the 'no-go' voltage threshold, and the engine started..... Anyone know what the charging system output is for the P5? The highest I saw with a quick search was 500 watts(po-po)- max- engine revved up. Do the math. Electric fuel pump- 60-80 watts. Computer and all the stuff it drives- around 60w (higher surges) Head lights- 100w ? Cooling fan- 80w? All the added lights and inverter- ? Charging system output at idle- 200w maybe...... I guess what I'm saying is, I'm very confident you had a low voltage issue caused by too much electrical load on the system.
OK, I'll shut up now.