I believe I read this somewhere, but I couldn't find anything. What's the timing on the crit effect you take from the asteroid?

Case in point: You go over an asteroid, bump into a ship and remain on the asteroid, all while taking a crit from the dice roll, which gives you Stunned pilot. Do you take an extra damage? The rules seem to indicate that you resolve your full maneuver (including checking for special conditions) and then you draw the crit. I'm not 100% sure though. Any ideas?

My thought is that getting the card is still part of everything and that because you hit that card's trigger you will then suffer the added damage.

No.first you execute your maneuver. Then roll for damage and get stunned pilot. So the card does not trigger from this maneuver.

Stephen (of the Esven variety) has it right. Per page 20, you execute the maneuver as normal (which would include the overlap), then roll for damage.

This is why R2-D2 goes before the damage roll - he triggers from the maneuver, which completes before moving on to the damage check.