Sounds like you've taken a logical set of steps to try and isolate the problem. If functionally the injectors work in diagnostics mode, I'd be curious to know if the bike runs if you manually spray some fuel (with a spray bottle) directly in the velocity stacks? This would tell us that yes it runs, and yes fuel coming from the injectors causing problem. At the very least it would prove your hypothesis. If it does run with manual fuel fed in, its hard to say what the injectors are being instructed to do during the start sequence.
If you have access to one, an oscilloscope (which usually sample in the 2+ Ghz range) could be useful. Run it in diag mode, monitoring an injector (or all 4), then run it starting the bike. This will compare the signal being sent to the injector under each case. Its possible the diagnostics and start sequence are not one in the same. I would then flash the ECU with the stock settings (save your current flash if you can) and run the same test again. This will give you the delta between the 3.
I think your right, seems like the ECU is not telling the injectors to spray. I haven't worked on a 2013 to be honest.
Chances are there is some input into the ECU preventing it from firing, as you've concluded. Perhaps try to find someone that can lend you an ECU. If it works you know its the ECU. If not, you know its an input to the ECU. Consider using another battery as well, e.g. a car/truck battery. I know a few bikes that refuse to start as soon as the voltage drops a bit, although you said it starts strong. Either way, start with the simple things first.
nothing worse than a bike not starting. Just a few ideas to help narrow it down further. A look at the wiring diagram may help as well, tip over sensors, blown fuses, kill switches, kick stands, faulty relays are the usual culprits.