Deducting Federal Income Tax from State Income Tax Liability

Context: I am calculating what my taxes will be next year (2021) for purposes of filling out my W-4s such that my withholdings will be as close to my actual tax liability as possible, to minimize my tax refund. I live in Oregon.

I am going to be itemizing deductions for the tax year of 2021, rather than taking the standard deduction. This means that I can deduct my Oregon income tax (OIT) from my federal income tax (FIT) liability. However, in a handful of states, including my state of Oregon, I can also do the reverse: I can deduct my FIT from my OIT liability… which will then in turn re-affect my FIT liability, which will again re-affect my OIT liability… in other words, it creates a seemingly circular dependency.

My question is: What is the correct way to resolve this? Or, more specifically, Is the way I resolved it, the correct way?

My solution was to first calculate my OIT liability without deducting FIT, and then calculate my FIT liability including the deduction of my OIT, to get my initial calculated amounts. These were approximately an OIT of $4400 and an FIT of $5000. I then recalculated my OIT by deducting my FIT, and then adjusted my FIT wit the new OIT, and rinse and repeat until I reached a stable amount for each tax liability where the result of adjusting the one no longer changed the amount of the other. The end result was an OIT around $3900 and an FIT around $5100 (in other words, about $400 total less than owed tax than when I started).

So my question is, is this the right way to resolve this circular dependency, via recursion?