As a follow-up:
I updated to the latest version over the weekend and it solved my draft freezing issue in Franchise Mode.
It looks like Ryan Mantha was moved from the being Draft eligible to Free Agency. The draft did not freeze and I was able to get through the draft without it freezing.
To be clear, I did not have to start a new Franchise Mode. This latest update allowed me to continue with my existing Franchise game, so a big shout out to whoever at EA saw this thread and was able to resolve this specific issue.
I'm not sure if this also resolved the freezing for BAP, but for the draft in Franchise mode, it worked for me.
February 2017 - last edited February 2017 by EA_Barry
This is a roster issue. There are only so many spots your team can have for players. The [Edit - Admin.] who work this game have failed to install a safety catch that limits or warns you of this. You need to dump your 7-5 round draft picks, sign or dump unsigned players and generally trim your roster BEFORE the draft. This will fix the issue. EA owes me.