I found a local TV repair shop (dying breed unfortunately) with two half-strips that were the right type, for a very reasonable amount. When installed, I now have all 4 strips continuously lit (32 LEDs) total! Major milestone event. Voltage across the backlight = 98Vdc, which is 3.06V/LED and well within the BL drivers rating of 130Vdc @ 750mA. Not sure of the loop current. V open-ckt is about 225V if I recall correctly. With the damaged half-strip installed the voltage across the backlight string meas. 190 Vdc!
The BL problem was this half-strip began drawing far more current over time than the others, the LED BL driver sensed this and raised the voltage which over time caused the burned area. As it burned, the trace resistance increased due to the rapidly shrinking strip width caused by arcing vaporizing the copper. The PS detected this increasing resistance, and raised the voltage even more. The LED BL driver behaves like a constant current source and therefore will raise the voltage to attempt to keep it so. However, it does have limits. So do the LEDs and copper within the strips. When V & I get too out-of-whack, the wheels come off, LEDs will burn, as will the copper foil, and the PS shuts down.
Problem here though is it didn't shut down soon enough to prevent arcing, which is a fire hazard!
I attempted to rig the defective strip with enough resistance to keep the PS on for testing, so I replaced the shorted end with about 30 Ohms. Problem is a resistor isn't a diode or LED. But I also didn't have several 3W diodes on hand. The damaged strip lit like all the others. The problem though it was drawing far too much current. Voltage testing sometimes won't find faults that current testing will reveal. Even with a 500 Ohm R across the end, it still drew too much current.
So the backlight is now fixed.
However there's another problem elsewhere, perhaps in the timing-control board. More on that later.