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Re: PhD Economics or Public Policy Profile Eval
For top ranked programs, without a letter from a well-known economist, you may get filtered out because of the C in Calc II and the B's in the other math grades. Your quant GRE score is also on the margin for top 20 schools. Retaking the GRE one more time might have higher returns for your profile, because a higher score will help alleviate concerns over your math ability.
Regarding how this impacts your chances at lower ranked school I am not sure. I do know however that almost all credible programs care a lot about your perceived ability to pass the first year, and math grades matter a lot for that perception. Also, a master's in public policy will probably not count for much, and might even count against you at higher ranked programs.
You seem better suited (as you mentioned) for a public policy PhD. These PhD's, while different, offer some advantages over econ PhD especially for those interested in government work. I would check out the public policy programs at well-known schools as well as Pardee RAND Graduate School, which offers a PhD in public policy. This PhD program seems to give more credit to people with work experience, and they will also surely count your masters for you rather than against you. They finally have very good job placement in the government and think tank world. They have a pre-application where they will rate your chances of admission up-front which is very helpful.