Congrats on acceptances! I think the main factors that are pushing you one way vs. the other is SO/family but more cost in Boston vs. graduating debt free but further away from family/SO.
A long distance relationship from coast to coast sounds miserable, especially with time difference. If you are super serious about your SO then it might be worth staying at Harvard given the extra cost. Also, what are the possibilities of them moving to the Bay Area?
Finally, in terms of financial aid, HMS is not really known to "match" scholarships, but it seems like they are receptive to hearing about need-based aid from peer schools. It might be worth reaching out to them to see if there's anything they can do. 125k is a well below average amount of debt, but at the same time it is still significant especially if you end up going into primary care or academics.
Ultimately both are obviously great schools, and you'll be fine either way; think more about how important being close to family/SO is for you!