Tough one RumbaToMD. SOPHAS does allow you to e-submit prior to submission of references. In such a scenario, it is my understanding that they go about calculating your gpa and then send out the documents when the references respond. By waiting to e-submit, SOPHAS will almost assuredly not send your app to the schools by 1/15.
However, I'm not sure if the schools will count your app on time based on when you e-submitted, or based on when SOPHAS sends it out. Furthermore, depending on the school, the deadlines may not be set in stone (some schools have rolling applications, but still list deadlines). All you can do is hope for the best. You might consider contacting a professor or academic coordinator at the school in question to let them know your app is on its way. Good luck!