So in case it helps anyone in the future, my final version was as follows (the letters have changed because I'm working with different cells now. In these examples, M6 is the active cell):

=AND($M6="",TODAY()>=DATE(YEAR(TODAY()),3,31)-45)

That conditionally highlights cell M6 if today's date is within 55 days of March 31st of the current calendar year. I added a couple more rules to highlight different colors when the cell is still blank within 30 days and 15 days of quarter close.

To do the next quarter, you just change 3,31 to 6,30 for Q2, and so forth.

If you don't want the condition about the cell being blank, I believe you could just use:
=TODAY()>=DATE(YEAR(TODAY()),3,31)-45