As far as I know and some things are officially verified, the invasion was almost imminent in early Dec. 1980. The reaction of the POTUS-elect only postponed the Soviet plans till all things would be made clear. The assassination attempt of Reagan scared the Russians to death not to be accused of the organizing, preparing or even conducting the attempt for fear of the possible US retaliation.
So, Jaruzelski was given the order from the Kremlin to stifle the Solidarity, yet, as you said, he begged Moscow for the invasion as he didn't believe in the loyalty of the Polish forces.
You’re right, that there was a very good chance of invasion in 1980, before Reagan took office. But once Reagan was there, the Soviets basically told the Poles they were on their own.