Fred, a thought - since you own a GS-911, try connecting it and seeing what the fuel pressure is just before the bike is started the first time, then compare the value to just before the bike is started the second time.
What I'm thinking is that maybe, the fuel pump doesn't prime the fuelling circuit when the ECU receives the 'Ignition On' signal - but only when the starter button is pressed.
This may explain why it only starts cleanly the second time the starter button is pressed - because that second time, there is now residual fuel pressure in the system.
...Let us know?
When I bought my K1200S in 2009, I was puzzled by the fact that the engine seemed to turn a few times before it caught - always.
Then I read a tech article that said that's a diagnostic feature built into that engine - it will always complete at least three revolutions before the ECU gives the okay for fuelling and ignition. It needs that time to check all engine-related sensors and actuators.