Does anybody know the timeframe for how long a compassionate reassignment takes to get processed at HRC?

You should have an answer within 30 days of your request getting to HRC. The slow part is usually getting the recommendation through your brigade.

Reassignments like this are unique by design. They generally take a week or so but it all depends because they are like snowflakes and each one is different in it's own way as circumstances are always different. I would recommend working with your leadership and your S-1 to navigate it together. There isn't a cookie cutter frame that will fit it. Just be the squeaky wheel