Another method, OP, is that your family can get into the Fort past the guard if they tell him "We're here to see the Smith family in site #1614" (which you will have told them in advance). They can park in the day lot or down to your campsite if you have room.
Have a great Tgiving dinner. We did Thanksgiving with lots of family 10 years ago in loop 1500 (actually on the Saturday after Tgiving). Hosted 15 people and served a 20# turkey out of my pop-up camper.
You'll make some great family memories for everyone.
Have fun!
Bama Ed
PS - I bet the 5k is pretty informal. It may require sign-up in advance or day-of but your family can put down your site number (if required) since they will be your guests on that day.