My first thought is that an injector is leaking/sticking open. That would drip fuel into the intake until the fuel pressure drops.
Depending on how bad it's sticking, it may be dumping a fair amount of fuel into the intake. But even a little can upset the restart idle/RPM.
It could be something else, but this is just my best guess.
I would say, if I'm correct, that bringing it to a good mechanic would be your best course of action here. It won't correct itself.
Don't "think outside the box".
There is no box.
Do it correct, or do it twice.