I had a similar problem on a '05 WideGlide at 7,000 miles. On '05 WG, you had a choice of carb or EFI, I chose EFI. Same as others mentioned; fuel line in the tank had a hole rubbed in it. No codes. It would run fine at idle and small throttle openings, but at larger throttle openings, it was running out of fuel. What confused the situation, it was running fine, then we tore it down to go from 88 to 95, S&S 585 gear drive cams, roller rocker arms, 10.5:1 CR, big heads, etc. Put it back together with a map that should've been close enough to break it in for a few miles, then we'd put it on the dyno. First ride, I was impressed to 3,000 to 3,500, then it'd fall flat. I kept thinking map was way off. Took it to the dealer, they turned the ignition on, waited for the fuel pump to pressure up and shut off, then just waited instead of starting it. Within 10-15 seconds, the fuel pump kicked on again, then off, then on, etc. Before they ever opened up the tank, they said "bad fuel pump". I said "fine, fix it, its still under warranty". They pulled the pump out, line had a very small hole in it, pump was fine. Bike now has 46K miles on it, no problems since.
Good luck, I hope you figure it out!