The sending unit in the tank is basically a simple variable resistor, so the numbers you gave as an Ohm reading do have meaning. I have no actual idea what the reading should be, but the fact that you have a variable reading at all is promising.
try moving the float up and down slowly, and look for the readings to fluctuate wildly, drop to 0 at a certain point or go to an infinite reading.
Personally it sounds like the gauge is bad. The jump from E to way over full, tells me the electronics is bad, and only registering voltage spikes as you turn the key.
But one more relatively quick check would be to find out which pin on the gauge cluster is used for the sender, remove the connector and take a voltage reading there. Have a buddy slowly move the float on the sender up and down and watch the voltage change at the cluster connector.
Maybe take an Ohm reading across the gauge inself and see what you come up with, then maybe hit the junk yards and at least take the same ohm readings on a donor gauge cluster.
Thats all I can think of right off the top of my head.
