I have a final update:
This was a weird one. When I bought my parts, the Ford place told me this was unusual, but not unheard of.
Follow along with me as the story did not end with a new battery. It ran fine for 3 days, then died at church. At this point I christened it the Antichrist.
No fuel. One poster was surprised I didn't test voltage at the inertia switch. He's wrong, I checked it many, many times. I even rigged a light that I could see from the driver seat and had power at the inertia switch. No fuel. I was still not convinced it was the fuel pump, but we replaced it and success! - for one day. Now it will start and run for about 2 - 5 minutes and then die. Futzing around back there, I lightly tapped the inertia switch while it was running and it immediately died. AHA! So we found an inertia switch, plugged it in and it ran for another day before stranding us. It has earned it's new name.
OK - follow the trail to the solution. Test light shows power at the inertia switch. In a eureka moment I grabbed a 12V motor and plugged it into the inertia switch. NOTHING. But the test light still works! So, Houston, I have problem between the inertia switch and the fuel pump. It shows 12 volts, but it cannot carry the load.
3rd time's a charm, so down comes the tank. I ran a ground lead directly to the fuel pump and jumpered the power from the existing harness from the inertia switch. Pump runs!! I deduced there is a bad ground either at the fuel pump plug or in the harness.
I got a new inertia switch plug and fuel pump plug from Ford ($80 with my discount - ouch). The plugs came with crimp connectors and high quality heat shrink. I went ahead and soldered everything. While I was at it, I connected an additional ground wire from the pump plug to the chassis. Interestingly, the original plug had crimp connectors on the power and ground leads to the pump, but there were no splices in the fuel tank wires. I finished everything up and it is currently running, although it hasn't regained our trust yet.
I'm hoping this will be my last post in this thread, but the takeaway is -- If you have voltage at your inertia switch but the pump doesn't run, you may want to put a load at the inertia switch to see if you have a bad connection.