OK, I think I understand what SBM is asking. Reading this again:
I want to sing the harmony myself. Because the software simulation does not sound good.
However, the problem is that I can only remember the main melody.
So I wonder if it is possible to generate a third and then I sing the harmony along with the third.
What I think SBM wants is for BiaB to generate a harmony that (s)he can sing in his/her own voice and record to another track.
If I'm right, then I think the harmony generator should probably do that OK if SBM picks a suitable non-chordal instrument, maybe Saxophone, trombone, or whatever. Mute the melody or solo the harmony, listen in headphones, record own voice to a utility track?