So I’ll take a stab at something the Alliance could do to make it seem more “morally grey.”
As mentioned many times on this thread, anything the Alliance does to the Horde by this point will be cheered on by a significant portion of the Alliance playerbase. So here’s my solution to something that the Alliance players should also be able to agree is bad.
Make the Alliance leadership* do something that hurts innocents in the Alliance.
And make sure the Horde sees it.
There actually was quite a bit of Alliance-on-Alliance nastiness back in the earlier days of WoW. The grievances of the Defias Brotherhood, the dire situation of Westfall, the noble squabbling encouraged by Onyxia, the corruption of Archbishop Benedictus … I’m sure there’s more. But it was all internal to the Alliance, so when facing up against the Horde, they could pretend that it didn’t exist. (Yeah, the Horde was in on the Benedictus thing, but he was a literal “Who?” to us.) By contrast, the Horde has always been completely unable to hide its own problems.
If some Alliance village gets the negative consequences of the actions of some Alliance leader–we can come up with the specifics later–then it’s not a case of bad people getting what they deserve, and it’s not done in response to the past actions of the Horde.
And it’s absolutely imperative that Horde players see this event, or else it won’t stick. Bonus points if the Horde PC can somehow help the victims or even recruit them as a friendly allied group, perhaps creating a Horde-only flight point at whatever refugee camp they set up.
*If necessary, create a new character for this purpose. But if you do that, make sure that character sticks around and isn’t immediately killed off.