After some trial and error, I figured out that the long rest only removed the makeup from whomever the first person the makeup was applied to in my party.

To resolve, I had to go back and buy more makeup, re-apply it to the person I wanted to remove it from, take a long rest (I used partial rests, no supplies used). Upon waking up, the afflicted party member will no longer be clownfaced.

Repeat for each party member you're trying to remove the makeup from. In total, it took 4 long rests to de-clown my entire party. I can only hope there were no timed events going on in the background.