WARNING: SPOILERS
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All right. As it turns out, I have another quest bug to deal with. At the end of the civil war quest, after the siege on Windhelm, I break into the castle and confront Ulfric. The battle ensues, and towards the end Ulfric is incapacitated. Tullius gives me the option of killing Ulfric myself or letting him do it, and here's where things go funky:

If I refuse to do it, then nothing else happens. Ulfric just lays there gasping forever.

If I accept and kill Ulfric, the quest seems to complete nicely. I get a little text from Tullius, concluding with him saying he needs to go give a speech. Unfortunately, he never does this. He stays rooted in place inside the Windhelm castle forever, with battle music playing in the background. If I leave there are soldiers outside who are waiting for a speech, but it never comes. The inside of castle Windhelm never changes - it's always Tullius standing there, doing nothing. I can speak to him, but nothing advances the quest.

Any fix for this? I've tried reloading earlier saves and everything. It ALWAYS happens.