The Genos (and Tyros) sets up DSPs via Sysex, Problem is those sysex commands are used on the 'Rhythm voices' Normally what I do, is record rhythm voices from Genos into Logic Pro, and later send Logic Pro's tracks back to Genos assigned to Song Channels.. So any sysex you may have recorded is not going to work, because it is written to be send to an internal rhythm track, not a song channel.
All sysex has a 'header' which tells it what manufacturer, what model synth, kbd, and eventually MIDI track to talk to. I also believe that DSP specific details are not send out of MIDI port, but kept internal. (not positive or can prove it)
Sysex is too complicated for me to figure out.. It is usually written in Hex base, not decimal base (16 numbers, instead of 10). Some once wrote a sysex command program..
WHAT you can do is assign your DAW to send out on MIDI channels (I leave the MIDI channel the same as what Genos puts out). and in Genos assign those midi tracks to the rhythm voices, (Rhythm 1,2 Bass, Chords 1,2, pads, phrase 1,2). So when you call up a voice, the right DSPs will be assigned. But I suspect, this is not what you want to do.
On the Tyros manuals, only certain DSPs went to specific channels or rhythm tracks, Now on Genos, all DSPS go to song channels 1 - 16. So I am suspecting there are additional DSPs, for the left, right 1 - 3, and rhythm tracks..
Cause none of the 16 editable DSPS can be sent to a style part. (or at least I can figure out).. This would be something to talk to Yamaha techs about, it may be beyond the area of where they can help you.
If you can do it, the answer lies in Sysex control of DSPs. but I suspect that another group of DSPs are set aside for internal rhythm voices, (again not provable, on my part).
Sorry this is not more helpful.