I did essentially the same upgrade (20” iMac 7,1 completed Dec 2018, but I used the BCM9430CD Wifi/Bluetooth card - not that it should make any difference ) and have had no such problems with sound (I’m using Mojave now, but I did go through Sierra and High Sierra previously) . Occasionally, the computer will boot up and show “Bluetooth unavailable”, but I run the maintenance actions in Onyx and then its ok.
Only suggestion I can make is to re-run the “Post Install app” and see if that improves anything and try Onyx as well.