I repaired a 2009 iMac gpu the same way with a heat gun but that was good for two years each time the first two times and didn’t work the third time. It’s worth a shot if you strongly suspect broken solder ball.
Same here, for the same equipement. Did not use heatgun but oven, wrapped in tinfoil. Same results as you reported. Finally sourced a compatible GPU from eBay, an ATI 5xxx from the next model year iMac. It was much much cheaper than sourcing an ATI 4xxx.
Opening the iMac the first time was very stressful.
