How about a rheostat in series? Put it between the gauge and sender and just dial additional resistance in to read E when you run out of gas. Let F end up wherever as E is more important to me. Feasible?
This will not work. I tried 3 or 4 times, in series, in parallel a combination of both.
The problem is the gauge is a bi-metal resistor. as it heats up it uncoils. The problem is the resistance characteristics of the resistors have changed over time and use.
You need to work with the resistance that is given, it is like a worn out car, in order to get it up and running you have to give it more gas.
In the meters case the gas is equivalent to the voltage. give it a little more gas and it will still run like before.
Increase the voltage and you meet the meter on its terms