Great question about the BWT, Sonny! Part of the increase is likely due to great production last year when the prairies were also wet although not this wet. Additionally, there was probably a movement of BWT from areas outside the survey area, e.g., Nebraska, Iowa, onto the survey area.
Yes, some, but not all, female Redheads are parasitic and lay part or all of a clutch in ( primarily ) Canvasback nests. It is mainly first-year females that do that. But, like all prairie-breeding dusks, Redheads are in pairs when the survey is done and the pairs are what is counted.
You're correct -- the counts are of the number of breeding ducks and given good production, which is to be expected this summer, the fall population will be 2-3 times higher than the spring breeding population.