Filling up at the gas station

I have trouble gassing up my 1964 Plymouth Valiant Signet. The filler nozzle leans way back, causing the pump to shut off even while I'm squeezing the handle. If I turn the nozzle upside down and hold it firmly into the opening, I can get it to keep pumping and filling. But I have to guess when it's close to full/shutoff, because if I wait for it to shut off automatically, right as it shuts off some gas overflows and runs down the side of the car. Any suggestions?