Thanks everyone for the inputs so far.
Did a bit more digging overnight (with the help of a Hungarian colleague), and have found this place too - about 60km south of Lake Balaton and 80km south of Tapolca (which was 2./NSGr.10's location in March 45), which could be a better candidate for the location:
https://www.mindat.org/feature-3044127.html
The date and the location makes me think this is more likely an operational flight than a liaison or hack flight and brings me back to my original thoughts about it being misreported as a Bu 131.