That’s been done. I think there’s a package—the homenet people from Cisco were working on it a couple of years ago. I haven’t had good luck with it—it works in some cases, but if for example you have a device that defends its hostname that happens to be connected to both sides of the router, bad things happen. That’s not the only issue, but it’s one of the more obvious ones.
mDNSResponder/dnssd-relay is not an ideal solution to the problem because mDNSResponder is rather large and does more than you need, but a more compact mdns implementation like the one that was being worked on for openwrt a while back could work with a smaller footprint.
What you might want to bear in mind is that as the network grows, multicast bridging gets less and less good. Multicast is not reliable, and it slows down the whole network when you use it, so if there is a lot of multicast traffic, all traffic is impacted. Also, each hop along the way multiplies the unreliability, so while for a single hop it might not be bad, if you have a couple of routers, as in a mesh configuration, it starts to get bad.
What I pointed you to is definitely useful, but not complete. This is why we’re working on it at the IETF hackathon. It will do what you want, but it could definitely be improved. We’re using the AR750S to prototype this—if you look at the Apple WWDC presentation on Wide Area Bonjour, it actually points to this page which suggests the AR750S for people to use for testing. 
You can see the WWDC session here: Advances in Networking, Part 2 - WWDC19 - Videos - Apple Developer