Capital gains when moving state

Hello,

During 2020, this happened:

1. In March 2020, while living in California as a resident, I realized a capital loss of -$80,000 due to stock sale
2. In April 2020, I permanently moved to Illinois for a job change, and took all the steps to change my residence
3. In November 2020, while living in Illinois as a resident, I realized a capital gain of $300,000 due to stock sale

I am trying to understand how these gains will be split between these states.

If I follow the rule where stock capital gains are sourced in the state of residence, the split should be -$80,000 to CA and $300,000 to IL. First question: is it normal that I will have to report a $300,000 to IL, while for federal returns I’ll use $220,000, so much lower? Looking at the forms it is not completely obvious it is the right thing to do, and I would obviously love it if there was a way to legally "shift" these capital losses to IL, since I don't have any capital gains in CA to offset, so these would be lost.

I also have a federal + CA capital loss carryover of $5,000 due to stock sale in previous years, and, if I’m understanding things right, this will go to California prorated by the number of days I was a CA resident (so something like $1250, assuming I moved in April). This is because, when the carryover is re-evaluated as if I was a CA non-resident for the previous years, it becomes $0, since it wasn’t related to CA property. My second question is: is this carryover calculation correct, and am I right in not allocating any of this carryover loss to Illinois? I couldn't find anywhere the rules that state if previous year loss carryovers need to be restated when one becomes IL resident.

Thanks