COVID-19 401k distribution and moved States

A bit of a unique situation created by the pandemic, and I’m having trouble figuring out how to pay estimated taxes as a result. I qualified to take an early withdrawal from my employer sponsored 401k because the pandemic. Since the withdrawal, I moved from NY to NJ. The withdrawal was taken while I was still a resident of NY.

 

Id like to pay the tax due over three years, as allowed by statute, however I’ve run into a conundrum. For state tax purposes, I imagine I will include the 1/3 portion in my part year resident return for NY. However, the way tax rules are set between NY and NJ 401k withdrawals would be taxed by NJ,  not NY after becoming a NJ resident. So - basically this year I will pay the 1/3 to NY, but if the IRS isn’t even going to consider the other 2/3 as part of my income this year, would I need to pay subsequent year taxes based on when the distribution amount is taxed (so NY for 2020 and NJ for 2021 and 2022), or would I need to find a way to pay NY in 2021 and 2022 even though there is no mechanism to do so because I am no longer a resident?