Just did that route for urgent travel, when my primary passport was about to go to a foreign embassy for an unknown period of time so I needed a second passport. It was good they took down the online appointments page. The appointments all got taken by third parties, or by others who didn't intend to use them! The phone worked for me. They wanted lots of documentation for a second passport.

In the OP's case, I'd probably lean towards waiting until after the trip to renew. But renewing now could also make sense. If need be, your senator or congressman's office may be helpful if the passport doesn't come back in a timely manner.