Yeah, I did read the title, maybe I missed something. I hit a lot of posts..sorry.
You are heating the fuel rail, not the fuel lines all the way back to the tank. Think of a garden hose that freezes, most of the fluid can't get past the blockage to begin with, but you may have a trickle. Seems that you'd need to heat the line the whole way back. The lines from your rail to the edge of the body...are plastic and wouldn't conduct the heat very well, which seems odd for helping to thaw the lines.
Secondly if you had water in the tank/lines, the engine would run poorly.
Have you tested the pump for pressure at the fuel filter? That can help diagnose the lack of any pressure at the rail. Maybe you have a blockage in the filter or the pump isn't kicking on. I've only been working on cars for about 10 years, I've made a few tools and adapters to test these types of things. A piece of an old fuel rail (supply side) clamped into a tube and attached to the pressure gauge can be a great diagnostic tool.
There isn't any wiring on the engine that should be able to be heated and get the fuel pump to run or not run. That would be in the relay center on the right side strut tower.
