1. Use a Sonos Port to connect to the current amplifier. 
    
2. Depending on matching the impedance, you might be able to us a Sonos Amp for all four speakers. Or, at the least, two Sonos  Amps, and just group them together. 
    

Note: Sonos does not make any in ceiling speakers. They are a reseller, however, for a company called Sonance, which does. There is one line of Sonance speakers, the Architectural line, which allows three pairs of speakers to be connected to a single Sonos Amp. This is due to some collaboration during the design phase of these speakers with Sonia itself, but so far has not been extended to other speakers from Sonance, or to other company’s speakers. 

Thanks so much, Bruce!  So it sounds like the Port will allow the turntables to play to the current hardwired receiver/speakers and also to Sonos speakers in other rooms.  Will it also allow streaming music played via the Sonos app to play through the hardwired receiver/speakers that the Port is connected to? 

Yes, that’s exactly what a Port is intended for -- to stream music via amplified speakers (the system recognizes the Port as just another Sonos speaker essentially -- but playing through your wired speakers).  You need to connect the Port to your receiver and also the turntable to your Port.  Line out for the streaming to your receiver; line in for the turntable.  See below image (if you have a digital input on your receiver, you can use the digital  out - circled below - which is what I use):

Incredible, thanks once again.  You’ve helped me overcome a serious mental block.