Do we have a photo of the aircraft configured at 30° Flaps for comparison?
No. This is a screen capture of the airplane landing at Burbank in March 1937 after a test flight with Kelly Johnson.
The full 45° of flap appears to be deployed. As you can see, it's pretty obvious when the flaps are down. There were no flaps deployed at Lae.
Normal takeoff procedure for the 10E did not call for the use of flaps. Film of the takeoff from Oakland for the first world flight attempt shows no flaps deployed (and for that takeoff Paul Mantz was in the right seat and possibly making the takeoff). That was a heavy takeoff but Oakland had a long runway. It's all about speed. If the 3,000 foot runway at Lae had been maybe 500 feet longer she probably could have reached sufficient speed (around 100 mph) to rotate and establish a positive ,if shallow, rate of climb.
She's probably moving at about 95 mph when she sees the end of the runway approaching. (Collopy says she's 150 feet from the end.) Aborting the takeoff is not an option. She has no choice. In desperation she horses back on the yoke and the airplane lurches off the ground, but it won't climb out of ground effect. If she applies any further back pressure it shudders on the edge of a stall. Once she passes the drop off at the end of the runway the plane settles until it's back in ground effect over the water. It must have been awfully tempting to pull back on the yoke as it settled toward the water but if she had done that the flight would have ended then and there and we'd be trying to solve some other mystery.
According to Report 487, with 30° of flap the airplane should fly off at 90 mph after a run of 2,100 feet and climb at 500 fpm. The conditions at Lae were a bit different than at Burbank. Lighter weight but turf instead of a paved runway. Probably a little higher density altitude. I'm guessing the airplane would have come unstuck after a run of about 2,600 feet. Bob Brandenburg may be able to balance out all the variables and give a more informed estimate.