> My reading of how mDNS works is that it should suffer from similar problems to SSDP on routers that can't broadcast/multicast between radios

This smells of someone who is not a network engineer. mDNS works fine, it has known ways to route it across broadcast domains, and actually, way more products out of the box can "reflect" mDNS across VLANs than SSDP. What on earth does that have to do with broadcasting "between radios"?.

> This is because the speakers all know where each other are on the local network (thanks to SSDP),

But you just said above they switched to mDNS?