Jim, if possible, can you run an extra ground wire between the tank and the chassis? Is the temperature gauge (assuming it's electrical) behaving normally or has it started reading low also?
NardisCNC, in your case, it sounds like the sending unit wiper is coming off the resistance windings inside the sending unit when the float is all the way up. I haven't worked on Midget sending units but most others I have tinkered with have upper and lower limit tabs to keep the float arm within a certain range. In all likelihood, you could re-bend the upper limit tab on your car's sending unit so the wiper never moves off the windings. However, if you have to drop the tank to do this... it doesn't seem worth the effort.