You are forgetting that record keepers are notorious for making and following their own rules that don't necessarily conform to the regulations or the instructions of the trustee/Plan Administrator.
About the withdrawal: these are trust accounts, and the Trustee should have the say of who can and cannot take their money. It should be up to the Plan Administrator to follow prudent plan policies as to what is needed to make a distribution. If the Trustee is satisfied with those policies and is confident they have been followed, it should approve the withdrawal.
Proposed strategy makes sense to me.
From what little reading I've done just now: If we could go back in time, we'd treat the $8000 as a Roth conversion, put it in a Roth account and then immediately recharacterize it back to a traditional IRA. But the proverbial cat is already out of the bag.