Thanks to a417 getting me on the right track for troubleshooting, I think I'm understanding the nature of the problem now.
Using SDRUno, "Monitor Source Audio if No Sync and Signal Present" wasn't working at all. It was full-time static. I made sure I had no filters. I tried some other things until I stumbled onto switching from narrow FM to wide FM. Under wide FM "Monitor Source Audio if No Sync and Signal Present" started working in SDRUno. From here, I started adjusting the bandwidth while still in wide FM mode. As soon as got down around 8k bandwidth, SDRUno feeding into DSD+ started behaving exactly the same way as the scanner discriminator tap: random little bursts of static.
My hypothesis is that the Pro 163 is also wide FM mode (
another thread confirms this) and is around 8k bandwidth. This I can't change. So, it seems that DSD+ needs FM wide for "Monitor Source Audio if No Sync and Signal Present" to work at all. And even then, it needs somewhat more than 8k of bandwidth so that it doesn't get confused and let static break through sporadically.
My question now: is there some aspect of DSD+ that can be adjusted to deal better with 8k-ish bandwidth while using the "Monitor Source Audio if No Sync and Signal Present" mode? (I've already played with the audio bit rates under Windows with no luck.)