If you want to test it out for free, just clip a wire from the sending unit line to the fuel line and see if your gauge changes. I doubt it'll correct your 9 gallon fillup problem but adding a strap definitely won't hurt anything.
The line on your sending unit looks pretty shiny. Do you know if this is an aftermarket sending unit? They're notoriously inaccurate. They require removing and bending the arm to get accurate read outs.
My car has an original one and it stays on Full for the first 50 miles and then drops from Full to Empty over the next 25 miles and stays on Empty until it's actually empty. I don't think anything can be done about that.