The good folks at d3playbook.com let us know that a group called NACAC, the National Association for College Admission Counseling, publishes a voluntary
list of colleges that still have openings which is updated daily. While the web site allows some filtering it's best to download a CSV and use your favorite spreadsheet or other tool if you want to really poke at the data. Looking at private institutions you will unsurprisingly see a good number of D3 schools still looking for bodies, and in the public arena a few of the UW family are still open. Of schools based in the US, there are a *lot* more private schools still open (193 as of this writing) than public (89), though schools must be members of the NACAC to participate. There is a searchable directory
here if you want to see if a school is a member, though that doesn't guarantee participation in this particular program.