Campaign hand trying to break into policy

[DC20001]

I'm 27 years-old and work on the campaign side of politics. Of the five-and-a-half years since I completed undergrad, four have been spent working as a research operative for a mix of candidate campaigns, labor unions, and political action committees. I also spent a year and change working in an entry-level administrative role for a U.S. senator.

In the campaign world, research essentially means "opposition research," though it encompasses a wide array of other duties as well. It's basically a hybrid role whose closest analogue in the corporate and non-profit worlds would be a communications office (it's in the same general family as comms). 

I'm interested in fulltime MPP and MPA programs as a way to break into harder policy work.  Part of me would like to break into the advocacy space here in D.C. while another part of me is interested in a more technical path that points towards a government agency or a think tank. Both entail a career reset of sorts and would be hard to pursue without going back to school.

Is my experience really what the top schools are looking for? Looking over the student bios at Princeton, everyone seems to come from the government or non-profit spaces. Will they consider my campaign experience relevant? I'd also just be interested in hearing from anyone who's transitioned from elections/campaign work to policy via an MPP. Many thanks in advance!