Instrument mismatch with General MIDI output

You’re right, the two orchestral instruments that you mentioned don’t have a MIDI mapping in Music Studio. It was implemented this way in order to provide the best possible mapping on MIDI import, where the GM Flute should be mapped to the most generic sounding flute in Music Studio.
To improve this, we’ll have to implement separate mappings for MIDI import and export. We’ll keep that in mind as a possible future improvement, thanks for bringing this to our attention!

(ps: I also tested the contrary by loading a standard GM song into MS, then sending from MS to my synth and in this case everything works fine as expected. So it seems the issue just affects tracks created in MS from scratch.)

No, it really just depends on the instrument. After importing a GM song, Music Studio selects instruments that will perfectly map to GM instruments, also at export.