What resolution are you hoping for? If you are looking to move your flights earlier (for example the flight the day before with plenty of F availability), you can always ask and see what the response is. Unfortunately, due to schedule reductions and what not, most of the flights to STT in the days after yours are overbooked as well.

As mentioned above, if you'd like to stay on the current flight, the best thing to do is to monitor the reservation/seatmap and see if anybody cancels or rebooks, as it's likely that inevitably somebody will find that they ended up on your flight and didn't want to be.

Unfortunately, kicking somebody else off the flight to ensure space for your family is unlikely to be an acceptable solution at this point in time. Closer to the date, checking in at the 24 hr check in window may improve your chances of avoiding a downgrade

One last idea, though I'm unsure how it would work in practice, is to ask an agent to delete your own seat assignment and assign it to your straggling family member. In the event of an involuntary downgrade or rebooking at the airport, the options and/or compensation presented to you as an EXP may be significantly better than your family member, assuming they have no status.