FaceTime Problems with External Microphone

Within the past month (after one of the Catalina updates, either 10.15.3 or 10.15.4), FaceTime stopped being to access my external microphone. I use a number of other apps with the microphone (a Heil PR40 connected to a FireWire DI from Saffire with a pre-amp) and there are no problems with it (Audition, Audio Hijack, Saffire MixControl, and AmpKit, all fine). It is set as the system input in Audio-Midi setup. When I try to record the FaceTime input audio, it seems to be present but at an extremely low level, below -40dB. I have restarted my computer and FaceTime several times (and turned FaceTime on and off within the app), but never seem to be able to use the microphone with FaceTime. In the security settings, FaceTime does not appear to have any permission to use the microphone, which seems like a problem. Is there a way to force FaceTime to do that? Any other ideas for solutions would be most welcome.