When I plugged the various 1st boards in via pokerstove, my answers were slightly different for the outcomes on the 2nd board. I've stuck my numbers into your original post in bold.
Originally Posted by Eeyore
The odds AKo vs QQ are 43 : 57
In one play 43% of the time AKo gets all the money and QQ gets nothing, 57% of the time the other way around.
During the first run the most common situations are:
30% A/K hit and Q didn't -> 40.5 : 59.5 in the second round
4.8% AK hit and Q didn't -> 35 : 65
3.2% AA/KK hit and Q didn't -> 35 : 65
38% noone hit -> 46 :54
10% Q hit and A/K didn't -> 49.5 : 50.5
6% Q hit and A/K hit -> 44 : 56
I don't know the accurarcy of the weighted values, i.e. 30% A/K hits and Q doesn't, and honestly don't feel like thinking about it.
However, these new %'s for the 2nd board may be what you needed to reach what should have been the final conclusion, that EV is +/- 0 when running it twice rather than favoring either player.