This would be a hassle, but I would suggest removing the tank and taking out the fuel sending unit/fuel pump assembly and checking it closely for anything amiss. It looks like from the pics in my Haynes manual, and the exploding view posted earlier in this string, that the pump is connected to metal tubes running from the pickup screen, correct?
I would inspect all of the very closely, especially the parts closer to the pump, since the problem seems to occur when the tank is less than 1/2 full.
My guess would be that there is a crack in the metal tubes, or the connections to the pump inlet are bad, or something along that line, so that when the tank gets below 1/2, and you're turning left or whatever, the pump sucks air.
The centrifugal force of turns could cause the assembly to shift and thus open up a break somewhere, and the pump sucks air.
Once you get the assembly out of the tank, grasp it by the top and down by the pickup screen, and see if there is movement in it, and if you can see where something is broken, or loose, where air could get in the metal pickup tubes.
I was helping a friend with his Volvo once, and the thing wouldn't start when the tank got below 1/2. You could hear the intank pump run, and the other pump ran (It had 2 fuel pumps), but no gas.
We removed the intank assembly, and between the pump and the pickup, there was a 4 inch length of rubber hose, and the hose had a tear in it, so when the gas got below the tear, the pump sucked air and car no runny.
I have a feeling that your situation will be something similar.
1996 Olds LS, 198,900 miles: RIP...