Aside from the other advice here, reach out to potential advisors. PhD programs do not have hard and fast rules for admissions. If there is a person there who wants you, that is a huge boost.
Ultimately, what determines whether you are accepted to a PhD program is your CV and your LoRs. You usually need a GPA above that which the program states as a minimum, and they like seeing a GRE score (those programs who still require one) in the top percentiles.
Most important in GPA is your GPA for the courses in your major.
That counts for more than having a super high GPA. Is there anything published from that research, and does it have your name on it?
I don’t think that anybody will care - they are withdrawals, not Fs or incompletes.
Your GRE may be an issue, though.
However, if you graduated from a top program, that helps a lot. The Harvard Department of Government are obsessed with prestige, though not as much as they are obsessed with themselves. More than 3/4 of their faculty did their PhDs at Harvard, so I would actually think twice about doing your PhD there, unless you REALLY want to work at Harvard or at a place where the people in charge are also Harvard graduates - there is a distinct whiff of inbreeding going on there.