Odd note here, but the run-on issue was prevalent coming from the factory. GM's solution was to energize the AC compressor when you turn the key to "off".
When EPA forced the removal of lead from fuel, octane dropped and caused multiple runnability issues.
GM lowered compression, increased base timing to 14, increased base idle rpm, leaned out the mix. Then CCC (C3) came along to control emissions and knock sensors to retard timing when detonation was noted. Along with that went overdrive transmissions with super low first gear and high final drive ratio in the rear end, and locking converters.
On the Q-Jet... Yes rebuild your own. When ready to reinstall, turn the mixture screws out 1/2 to 1 turn from stock setting. This will richen up the idle and then will idle better and smother around 700 RPM. Problem should go away.