I've done a stall to stick push in the CRJ several times (in the actual aircraft on delivery acceptance test flights). It's really no big deal, and the aircraft recovers quite nicely provided that you have enough room to lower the nose a few degrees and SMOOTHLY apply power. Of course altitude wasn't an issue since we did them at 15,000'.
As mentioned before, the nose down tendancy when initially applying power is due to the engines being mounted above the longitudinal axis of the aircraft. Since the thrust axis is above this line (and above the "center of balance" from nose to tail), the addition of power creates "asymmetrical thrust" above the center of balance (if that makes any sense).
My recommendation on any maneuver is to go through it at a reasonable pace and not rush the recovery. Another good thing to do anytime that you add power from slow speed is thumb the trim for about half a second as you apply power. This is good for both the stall recovery and a go around.
1, because (in the case of a go around), it will disconnect the A/P. (Although pushing TOGA will as well).
And 2 because it gets the aircraft moving in the right direction as you apply power and counteracts that initial nose down tendancy. Once you get moving in the correct direction, then simply thumb it out (odds are you'll need to take out even more than you just put in, or the plane will do a tailstand and fly off like a homesick angel).
The sim is a bit squirrely, but in real life the actual approach to stall, shake and subsequent stick push is a nice smooth and stable approach. The nose drops before you even hit the buffet, and at altitudes where the air is thicker, the push isn't even that abrupt (maybe -.25g? If that?).