well, the answer is, it is very easy to pull this unit out of the wall (just a few screws on the sides and bottom of the front), and i happened to have a table just the right height to catch it. i popped off the back panel (which covers the entire back btw for anyone looking for this answer), and pushed the wire back through. i don't know why i was so intimidated by taking out the whole unit. putting the insides back together is going to take me way longer
thanks for everyone's help! hope this helps someone else in the future.