Great job! It is nice for the 1042 to be reported in the area that matches the form but the end goal is to have the correct income being reported and taxed.
What matters is for you to be able to show in an audit that you filed the income and paid any taxes due. Both the federal and state taxing agencies want to see the income and correct tax. They understand the location may vary and will accept your records/ methods as long as the tax is correct. Your question shows you are trying to do the right thing.
You do not want to be double taxed so that is not an option. I like simplicity, as you saw in my posts: but, you choose the method that makes you comfortable.
@JL_2021
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