Isn't it possible this would increase the chance they had financial ties to the nuclear industry? My initial thought was that if you appointed environmental scientists to monitor emissions in areas without nuclear plants, they could also check the work of other assessors in areas with nuclear plants, to make sure their colleagues were honest, when attending board meetings.
So you would get bright people which were otherwise uninvolved to check the work and listen to what was being discussed.
Another option which would not rely on local election, would be to have Congress appoint 50 environmental assessors, one from each state, which were required to be permanent residents of each state they were appointed to represent, rather than employees of a national office. The assessors would then meet once per year to form a national oversight board.