There are ublox chips that include compass data, but it's another 2 pins on the chip. I'd look at remote controlled aircraft sites, like drones. they make use of this data, to control position and where the camera is pointing.
I think drone software could give you what you want.
I also discovered yesterday that "carscan" can output the car's gps data, but I don't have the software to see if that includes compass bearing.
Or hang on I do, the U-Center app will replay all the data on the file. But I need to boot into a windows computer to play it. I'll have a look after I've done the dishes.
Keep your fingers crossed, this could be your answer.
BTW, we don't trust phone GPS data, they only use very small antennas, and can give strange results. Whereas the car GPS data is very good.
EDIT, but don't get your hopes up, I've just realised, as there's an extra two pins on the chip, it probably isn't a u-blox output, but goes to a second processor. I'll find out later
EDIT EDIT.
Sorry, no orientation info in the ubx file, hope you have luck with the flight controllers.