Channel Controller Volume Fine (39) doesn't work with General Midi Synth

I tried to use both volume controllers 7 (coarse) and 39 (fine) with General Midi Synth. It looks like controller #39 doesn’t work with this synth.
Fine volume just works with plugins:
Fader + Volume controller 7 (coarse)
A-amplifier plugin (just 20dB) + volume controller 7
Simple amplifier plugin and volume controller 7
What about controller #39? I would like to export midi file

It looks like fluidsynth does not use VOLUME_LSB (CC-39) for anything. Level control is using CC-7 only.

Expression (CC-11) might help for some voices.