This is extremely puzzling (as you are aware 
). My guess is that you need a new router or you think you are transmitting the SSID but in fact are not and fooling yourself into believing you are. (The latter was said without a condescending tone, but just meant as a constructive suggestion). Can you see your routers SSID on a friends phone etc. that has never been connected to your network?
When you say that
1) my iPhone, laptop etc can continue to see the router's main SSIDdo you mean that you can really see the router's SSID on the devices when you do a search? Or do you mean that they connect to the router OK? The latter does not necessarily mean that they can see the SSID because once a connection has been established, a transmitted SSID is not requited.
Also, for the life of me, I cannot see why connecting the Sonos with an Ethernet cable would suddenly make the router's WiFi SSID visible. The Sonos would just connect to the router via the Ethernet cable.
You also say
the router's main SSIDThis implies that it has more than one. If so, can you see the other one?
