I have always practiced a side step while drawing, but I can draw and shoot much faster when I go to my right, (right handed). I think any movement in an altercation is to the defenders advantage. Makes the bad guy re-asses, buys you a half second. I am sure there is a reason to go left or right based on the attackers direction, but my instinct to go right would probably take over. I think your recall about the muscles in the chest and shoulder are accurate. Moving to the attackers strong side, might make his control of a firearm more difficult, and tracking your movement a bit slower, as he would have to move his arm in a weaker direction, but so would you. But I don't think I can process info that fast if I am drawing a gun, I can barely process it now!