What you suggest is acceptable. The key is NJ law, which allows you to file either as joint or separate on the state return. And you come to a correct conclusion: by filing NJ separately, he may file a part-year return so that the Washington income is not taxed in NJ. (Note: both NY and NJ will factor in Washington's income to determine their tax, but they do not tax the income. Rather they pretend that all of your income is taxable and prorate the tax to the amount of income taxable in the state).
There's a lot of moving parts with the state return, but what you state is acceptable by law. To file a joint federal return and separate state returns, please note this FAQ: https://ttlc.intuit.com/replies/3301995
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