After several hours spread out over several days spent scouring the internet for information on this, I've finally found the setting on the Deliver page that was stripping the audio in my AAF exports from its metadata.
The Problem
I edited a project in Resolve. After ingesting, I used the Auto Sync function to automatically link the audio files from the external recorder to the video files from the camera, using timecode.
This worked brilliantly. I had to make a few small adjustments due to timecode drift during the day, but all in all, smooth sailing.
I edit my film, then it's time to deliver to sound: They want an AAF.
Resolve has a Protools preset on the Deliver page, which exports a reference video