Thanks to endorph, I was put on the right path towards getting voices to stand out against a bunch of ambient noises. Here's what I did to clean up the audio:
1) Find a five second segment of ambient noise on the clip, highlight it, and go to Effect, Noise Reduction, create profile
2) Select the entire clip, click Effect, Repeat Noise Reduction
That got me to a clean starting state with the file. Next, I used the Spectrograph to figure out what frequencies the voices I wanted to stand out fell under.
Then, I highlighted the segment of the clip with those voices and clicked Effect, Vocal Reduction and Isolation. I selected Isolation and set min/max frequencies of the voice.
After that, I used the Equalizer as endorph suggested, maxing out the frequencies I wanted to stand out and leaving the others alone.
Lastly, I went to Effect, Compressor and ran it on the file. I'm posting a complete answer to memorialize the steps in case someone else encounters the same challenge.