Keep the Demon Hunter starting zone exactly the way it is.
Simply make it in a storied perspective if your DH is a non-Night/Blood Elf. Instead of playing as your character on Niskara, you’re instead hearing the tales of the original Illidari during the BC era, and how they did all that stuff. (in reality, you’re just playing through it like as if you chose a belf/nelf depending on faction) Sort of like how we all turn into Humans for Culling of Stratholme Dungeon, to not bork the timestream.
Once the starting zone is finished, it fades from black to reveal that you’re outside the Stormwind/Orgrimmar Embassy sitting in front of Chromie who was telling you the story atop her giant hourglass. She reveals to you that since then, more defenders of Azeroth have joined the Illidari as a precautionary measure in case a new demonic/great threat of any nature should return to threaten her.
This alleviates the need to wait for Illidan to come back or the Legion to return or something, as well as opens the gates for what is technically already logically canon. Any other races becoming Illidari is simply a matter of devotion/commitment and really hating demons, which I think it’s pretty safe to say virtually every race did after the events of that expansion.