Wow. That sucks. I have none of these problems and my network sucks and is slow. I actually can’t buy more since my network only supports 10 WiFi devices at once. Between iPads, computers, phones, I have to disconnect something to get things to work sometimes but the homepods are quick to respond and always in sync. I have 3 minis and a og HomePod. They even work together flawlessly. As long as my phone is on the network.
The only frustration I’ve had is that they will play music separately from my phone. Sometimes I start the music on my phone, I’m doing other things on My phone and I try to adjust volume but it only adjusts the phones volume. I have to switch outputs and adjust etc etc. or I can ask Siri to turn it down which works, but I generally prefer using my phone. Took a while to figure out why I couldn’t adjust volume.