The fuel starvations is not too uncommon there can be several issues.
Probably most common is issues with the pick-up:
-1- there's supposed to be a pre-filter sock on the intake of the in-tank fuel pump - that pre-filter assembly often drops off into the tank after many years of constant vibration (in late '88 the fuel pump's intake changed from a hard ceramic to a more pliant rubber over steel design - well, those age and soften allowing the pre-filter to drop-off or losen)
-2- the pick-up is no longer in the "baffle", there's a small baffle in the tank to help with starvation (really you'll probably have this issue when cornereing left at pretty good speeds too!) - inside the tank, the return line is capped with a small rubber cone that stabilizes the rest of the stuff hanging in there (among other things) - that rubber can degrade and allow the pick-up itself to deform, though I've only seen this once on an XJ run with MTBE as a fuel additive.
The other issue is that the pick-up is centered latterally in the tank - sufficient force will draw fuel from that area (I mean the pick-up doesn't follow the fuel if the pump cavitates you'll see a stumble or the stall you discuss) - typically these symptoms show with roughly 7 gallons or less in the tank - your operating g-load/roll angle may be more severe, but ... Y'kinda do have to live in the physical world on some things...
Next time you're low on fuel (for me that's BELOW 1/4 on the gauge), remove the fuel-tank's sender/pump assy (ring is located on the top-front face of the tank - no need to lower the tank, but be sure that everything is celan so you're not filling the tank with sand or whatever) - inspect to see that your pre-filter is inplace and sealing to the pump intake (it should look like a dirty black sock sticking out at a right angle below the pump) - also look for the rubber cone on the return line... I'll wager that something is awry there...
If you end-up purchasing a new pre-filer, they'll oftne not seal/fit tightly to your pump's intake - since youv'e most likely got the rubber over steel intake on the pump you can use a steel guitar string to machine a groove into the rubber intake (I usually go about 1/8" from the intake end) and fit a 9/16" diameter x1/16" O-ring onto the pumps' intake then you'll find that the pre-filter fits and seals quite well indeed. (BTW there's kinda of a "key" cast into the outside diameter of the pre-filter's attachment to the pump so that you'll be able to get it installed in the correct orientation.)
On another note - is there any chanse that you have some contamination in your tank (fouling, water, etc)? And you have verified that your fuel filter is happy..?
As for the hintonsooner deal - that goes beyond sad - he should probably consider changing his user ID and starting over with his new commitment to not be an as$. There was no call for that - I hope one day to return the 'favor' to him or his wife when she's in real need of assistance.