Topic: Audio output through RME Babyface Pro not working in Google Hangouts

I'm having a frustrating problem that I can't figure out. When using Google Hangouts and a couple of similar services (Belive.tv, for example) in both Chrome and Safari, audio output through the RME Babyface Pro doesn't work. This happens on both my iMac and my Macbook Pro, and I even did a fresh installation of High Sierra on my iMac over the weekend, to no avail.

The audio output through RME works just fine in Garage Band, Skype, Zoom, and other applications so it's not a hardware problem. It works watching YouTube videos or listening to audio streams in Chrome and Safari, so I know it's not a browser-wide issue.

Even more strangely, in Google Hangouts before I start the handout when I click the "gear" icon and configure the audio settings to use the RME, and click the "play a test sound" link, I can hear the test sound through my headphones plugged into the RME. But then when I join the Hangout, I can't hear anything. Note that the mic/input going through the RME works just fine.

I have no idea what to try next, so hoping someone here might have an idea. I posted a message to the Chrome forums, but didn't hear back, and since the issue also occurs in Safari, I don't think it's only a Chrome problem.

Also, it's worth pointing out that I'm virtually certain this is a new issue. I've done Hangouts and Belive.Tv in the past with my current setup without issues. Could it be a problem with the most recent RME driver, or a new version of Chrome and/or Google Talk plugin? So weird.