Inspired by a post on the pianoworld forum, I started experimenting using a cheap Korg CM-300 contact microphone for directly picking up the sound from a soundboard rib.
I used a batteryless iRig HD 2 at full gain to connect the Korg CM-300 to my iPhone. I tried it on an upright, but it should similarly work on a grand.
So this could be a relatively cheap solution for somebody who wants to tune in very loud environments. The Korg CM-300 costs 12€ and the iRig 79€. An even cheaper alternative could be to use a TC-Helicon Go Solo instead of the iRig, which is only 39€, but I have not tried it yet.