With the chance that I may sound like a moron in consideration that you may have looked at the possibilities already, the fuel may be sloshing around creating bubbles. Since that is the only time that the problem occurs, the tank is almost empty and the maneuvers are somewhat violent...
I had the problem once on an old slow combat ship. I bought 15 "Sidewinders" from "The Bear" Bob Bearden. ( I do not know if any of you remember or know of him)
He was a really, really nice guy but smoked way too much for his health...it eventually caught up with him. Very sad...
Any time I did a sharp sequence of maneuvers overhead towards the end of the tank (3/4), my Fox would flame out. Not good for Combat
Had the typical Chicken hopper (from Bear's supply, the real TRW tanks then...) Tried different engines, different tanks, same thing. A friend suggested that I use a smaller diameter on the output tubing, use a smaller/closer tank to the engine or restrict the venturi by .002 in. (yeah, right; a square venturi!!!) I added epoxy to the diameter of the venturi (very rough and sloppy to do). He felt that there were 3 things going on:
The fuel pick up was too far back and even with the chicken hopper, the sharp turns would cause the fuel to be drawn back from the down acceleration while changing from insides/outsides.
The fuel was still sloshing around
Not enough fuel suction.
If you can, I would also check for tank leaks and also measure the amount of fuel you have left when it quits...
What fixed it? Moved the tank forward and the epoxy...
I may have repeated all the things you may have looked at... My apologies