I don't think her going mad is a problem. At all. In fact I'd wager GRRM wrote it that way.
But the way it was told was garbage, and it didn't have to be. Her father had visions, heard voices. So just literally put those in, like 3 times.
1: Scene where everyone is ra'ing Jon, focus on Danys face - have whispering come into the audio quoting from past episodes about never being loved in Westeros
2: scene where shes leaning against a pillar when Jon walks in: have more whispering as she stares into space, maybe this time the sound of flames and screaming from when she burned the dothraki tent. Then show her snap back to reality
3: when shes sitting hearing the bells , meld in Messeindei screaming draconis, then her yelling it various times, and ending with her eyes opening with fire reflecting in them.
There you go. All done in post, no need to film anything new, she goes mad.