Yes, a midi message is missing for that too…
A CC with values (0-63) corresponding to parts seems the best for me.
I think notes are already confusing ! 
There are appropriate to change patterns, hence parts. Only workaround with caveats.
I found a way to change patterns keeping their step position with Arranger and Song Pointer Position messages, but it requires a midi processor, and it is complicated to set up.
That way you can change parts on the fly. In example below if changed scenes, but it should work with parts…
Midi geekery…