Please keep us up to date on what you find. Not having an output to the PA is a major oversight on this product for me. There may also be a way to achieve this mod by taking a feed from the speaker through a resistor network, but as there is more than one speaker this may also be not that straight forward.
I looked into it a little bit more and I don't see a way out. I'm guessing that when a cable is plugged into the headphone out the Amplifi uses a different simulation set and then mixes all the signals - guitar, Aux in and Bluetooth - into something suitable for line out purposes. So, using the headphone out, all signals can be sent to a PA but the Amplifi speakers will of course be off.
Connecting a jack in parallel to the headphone out like I did and using this jack as a line out will keep the Amplifi speakers on and will allow the Bluetooth and the Aux signal to be sent to a PA with good results. As for the guitar signal, it's kinda weird. If you use only an amp and cab simulation you won't get the guitar signal. However, if you add something like a delay, chorus or reverb module in the chain, you will get a guitar signal to come out of the parallel jack but as far as I can tell you get only that portion of the signal and not the whole guitar signal. And it sounds absolutely awful if you feed that signal to something like a keyboard amp and play along with the Amplifi. It's like the two signals are out of phase or something. I double checked the jack connections and the two are indeed in parallel and not crossed. So I'm stumped for now. Again, I'm guessing that Line 6 didn't include a separate line out because this might overwhelm the Amplifi DSP.