I’m glad that Bluetooth streaming works for you now. Normally, the Bluetooth favorite should be automatically added to the Squeezebox server after installation. Perhaps this error is related to a specific Squeezebox server or Max2Play version. Which versions do you use? As you say, the dropouts can be due to the built-in Bluetooth chip. Do you use a WiFi connection? The simultaneous use of WiFi and Bluetooth is often problematic with the Pi 3. Apart from that, I can only recommend a Bluetooth dongle or, as you have already noted, the Pi 4.
If you are using the LMS 8.0, I recommend that you install the Wave-Input Fix on our Squeezebox server tab. Maybe that solves a couple of problems too.