I attended a UC Berkeley MPP session and they stated high quant GRE scores would help if no recent coursework. Many of these schools have a quant supplement where you describe your quant background to the admissions committee. The UC Berkeley admissions staff said, if admitted, students may be required to sit for the math exam to ensure they can follow along in classes. If you can’t pass, you have to do a summer bootcamp prior to the Fall which sucks. Clearly, it’s not a rule that you NEED the experience but I am certain it’s one of the many criteria they use for admissions decisions.

Based on what you shared, it seems like you have high quant GRE and have a lot of upside in other areas so it seems like you’d be a competitive candidate for many MPP/MPA programs.