I don't have such a problem with my version of the game; see attached screenshots of my Bone Dragons still having positive morale (from the Black Knights) even as they are swapped positions with my Guard Droids.
Version 1.2 build 5730; digital download purchase from Gamer's Gate.
I feel for those that do have this bug in their copy of KBAP... droids are quite powerful and would compliment a lot of army builds.
I haven't tried it out with morale-boosting items though since I don't have such items right now to test this. Perhaps this is just a bug concerning morale boosts from items? I mention this since you did say that morale changes from Dragon Despiser trait still shows. I'll see if I could test this further in my version.
EDIT: Whoops! Looks like I spoke too soon, I DO have the bug in my copy. But it is not an all-encompassing bug; for now, I can only confirm that it affects morale boosts from items; see attached screenshots of how Pirates with a morale boost from the Ring or Arianna lose the boost when transferred to a slot that used to be occupied by droids.
Good thing for my army I don't rely on morale boost from items.
Also good for me is that I haven't started building up the Mind tree; I'll just do it in one go, accumulate Mind runes for now, then see if the Voice of the Dragon still confers morale boost to my Bone Dragons.
As for a workaround, have you tried doing an uninstall and a reinstall? Just make a backup of your save game files first, though I think they are unaffected by an uninstall.