When you say SYnc the injectors, you mean Sync the throttles right?
DO you know what error codes were pulled off the ECU?>
I'm not too concerned with the battery, if it has enough juice to crank the engine it's ok. I would check the ECU voltage as this happens though.
As for gas filter, I know for a fact it won't make the engine stutter just lack power at WOT so rule that out. BUT I would change it just to see what is floating in the tank, many of us had parts stickers floating around in there from factory.
First stupid checklist:
MOST LIKELY: I assumed he cleaned any debris in the vacuum hoses BUT I would have him double check this as something might be stuck in the lines and would explain it all.
I also assume he checked that there is no mouse nest in the intake/exhaust.
Other thing that is common are the coil connectors, as the bike warms up can have an affect on a bad connection. I would check all 6