Apple Home just doesn’t work

My setup sounds pretty similar to yours, and as I added more HomePods, I also started having a little trouble with them. I know you’ve reported your wifi is good, but I solved our issues by experimenting with the network. And perhaps you’ve already considered all this, but I’ll give you the steps I took. Like you, I’m on all the latest software.

These are the steps I took. 

1. Ensured all HomePods are on the same Wi-Fi network. This one is pretty obvious, but our router had 2.4GHz and 5 ghz networks. I had sort of assumed they’d coordinate themselves to be on the same network and that we’d got a pretty clear notification if they weren’t, but no they were chugging away on different networks.
2. Experimented with 2.4ghz verses 5 ghz network. The 2.4 signal was reaching the furthest room a lot better, whereas 5 ghz is I understand faster. I moved all our devices to the 2.4 network and lived with that for a few days. Then moved everything to the 5 ghz network and lived with that for a few days. The 2.4 network was pretty poor, whereas the 5 ghz one was very good. Still a bit laggy with things like volume changes, but everything basically worked. The fact that 5 ghz signals aren’t as robust didn’t ended up mattering for us. 
3. Switched wifi router. I was using a new router from our ISP. I pulled out our old AirPort Extreme and set that up instead. And bang, our HomePod network was perfect. Both routers are 802.11ac, but the AirPort Extreme for whatever reason has proved to do a better job. 

Best of luck with your HomePods.

These are tips I have put together from Apple discussions and other sources. They included tips above:

Your router might be "too smart" for the Homepods that don't seem to be able to keep up with wifi optimising strategies. Try changing them to static IP addresses via your router settings. That made my system more reliable (but not perfect). + The original Homepod also seems to suffer from wifi problems related to "smart" routers/modem. Solutions included temporarily disabling the 5GHz band (to trouble shoot) and assigning a static (fixed) IP address. These are router settings and every router seems to have a different method of changing settings. As a start try typing 192.168.0.1 into your browser address field. This should load your router set-up page. The default user name is usually admin. If you are lucky there will be a help page for further steps such as enabling/disabling "smart connect".

Try assigning static IP addresses via your router settings. That solved some wifi issues with my Homepods.

Just realised there was a typo in my response. It should’ve read ‘My setup sounds pretty similar to yours, and as I added more HomePods, I also started having a *lot* trouble with them’.