So I started playing around with my Pro1-X again.
After the device being shelved for ~1.5 weeks, the battery is now at 61% and /sys/class/power_supply/battery/voltage_now never exceeds 3870000 µV. In this state, I cannot reproduce the speaker issue!
So, maybe, it indeed occurs only on brand-new devices (and batteries) where the voltage exceeds 4.1 V significantly after charge ... ? This might explain why the problem goes away after some time of using the Pro1-X.
edit: Re-charging the Pro1-X now, to check whether the problem comes back with battery full.