OK, I was trying the rail cleaning suggestions, and was still having problems. I was starting to suspect the pickup shoes were the problem. I tweaked them a little and cleaned them. That helped a little but not much. So I lifted up the rear of the car to put more force on the shoes. It made contact and ran, in most places that were otherwise dead! Set it down again and no-go.
I suspect that tilting it up that way creates pressure where the shoes hinge on the copper plates. That the shoes are not making good contact in the hinge.
But, to confuse the story more, I grabbed an AFX car, the fast ones, whatever they're called, and pulled the front axle off. This was to make it rub harder on the rails to hopefully clean them. It ran fine with few dead spots, which it ran past anyway because it's so fast.
After 5 or 6 laps I tried the T-Jet again, and it ran fine! I eventually ran the AFX car 15-20 laps on each lane and problem solved. Good contact on all lanes. This is after only cleaning a very small portion of the rails. 90% of the rails had not been cleaned at all, but the AFX car fixed it all. And the AFX car had no problem getting around on any of the lanes. It never stalled once.
Everything's good to go now, but I don't understand why the T-Jet had such problems while the AFX had none, and why the AFX fixed the problem the T-Jet was having. It makes no sense.