Those recommendations are tainted with political correctness and fearmongering rather than sound science.
Most sources have been tested for heavy metals and PCBs, and those with real problems usually have well known science based recommend for the quantities that are safe to consume on a regular basis.
In the rare case that a specific advisory says to only consume one serving per week, it is safe to consume one serving per week.
I've lived and fished and eaten fish in a lot of states with various advisories. Here is a link to the actual advisories on fish consumption in Louisiana:
http://www.deq.louisiana.gov/portal/...%202-18-09.pdf