There have been a few users that have run the digital smoker with a 900w modification using the Bradley controls, but I would not leave the smoker unattended.
Check you HD (Heating Differential) setting. If it is too high that may be causing the Inkbird to overshoot. You should set that to either 1 or 2 degrees F.
If overshooting is the only problem you can try bringing the cabinet up to temperature in stages. Such as bring it up to 150°F, and let it stable at that temperature, then bring it up to 225°F. That may reduce a high overshoot in temperature.
As far as your hookup, do you have the cabinet plugged directly into the Inkbird's Heating socket, the Inkbird plugged in directly into a wall socket, and the generator plugged directly into a wall socket?