I think that a new High King should be chosen for Skyrim that fits your choice in the civil war.
For example, if you're a Stormcloak, Ulfric is crowned High King and Brunwulf becomes Jarl, and if you're an Imperial, Elisif becomes High Queen. Only problem would be crowning a new Jarl to Haafingar, since Elisif remains Jarl both ways.

Couldn't Ulfric still be High King, but still be Jarl of Windhelm? Maybe Windhelm could become the capital city of Skyrim instead of Solitude.

I just want Ulfric to be replaced as Jarl xD