Is it possible to kill Ulfric after joining the Stormcloaks?

I have completed the Stormcloaks questline.

I headed over to Windhelm to see Ulfric, in the name of science. When you talk to him there's no option to challenge him to a duel or anything like that - he just tells you that you've done enough for now.

I tried attacking him, but he is like other "important" characters and cannot be killed. He just wussed out and fell to the floor instead.

There is one way that you can switch to Imperials halfway through the questline. I know that you don't want to support the Imperials, but it's the only option if you don't want to support Ulfric, unless you decide not to complete the quest chain at all.

After you retrieve the Jagged Crown, instead of taking it to Ulfric you can take it to General Tullius in order to join the Imperials.

Ulfric is an Essential NPC as a member of the Stormcloaks and therefore can't be killed.