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?
Yep, you'll have that. The cap/fill.location and the fill tube were designed long before there were auto shut off's on pumps.