Thanks for replying so late.
So, WAX206 sees mdns traffic on both 192.168.1.0/24 and 192.168.5.0/24 networks. I was hoping to see a clear indication of a query and the reply but nothing like that is clear to me. I'm not experienced with mdns and your traffic does not look like the example I saw on someone's blog.
Depending on what your last reply was, I was thinking of asking you to put your mac on a lan interface on the WAX206 but it looks like you did that already. 
If no-one else with avahi experience replies, it may be good to open a new thread with a title specific to this mDNS/avahi issue.
The next part I might be able to help troubleshoot is TCP connectivity to smart devices through the WAX206 (AP/router/firewall). Sometimes devices don't like routing setups like you have.
Does your r4s have a route table entry for 192.168.5.0/24 ?
Please show ip route show from your r4s.
If it does, Also on the r4s do traceroute 192.168.5.1
and traceroute 192.168.5.198 or some device IP you know is alive and should reply.
With your current setup, you might need to add the route to network 192.168.5.0/24 via 192.168.1.3 to all the devices in the 192.168.1.0/24 network. That might be fairly easy with a DHCP option.
An alternative would be to move the routing/firewalling for 192.168.5.0/24 to the R4S and trunk it back from the WAX206. These ideas for changes are only if needed though.
...till Sunday...