So what is imputation as used in Scripture.
I think that you are splitting hairs over what amounts to no difference. By definitions, I don’t see any difference.
If you don’t like the letters arranged to make the word impute, don’t use them that way. But it is a biblical term. It can fit into your vocabulary if you will give it any opportunity.
I view this sort of argument you are making as equivalent to saying that Jesus was from Bethlehem and could not have been from out of Egypt or from Nazareth. We know He was all of those because they are not mutually exclusive.
If you could explain why washing and imputing are mutually exclusive, it would help me know where you are coming from.
I like to think I am drawing distinctions to convey truth.
Imputation is the same as saying something is so. I can say some truth is so, and I you say something that I believe is true, then I can say or credit or declare your statement is true. Thus you have been imputed with a true statement. Abraham's faith was imputed to him as righteousness, or in other words he was declared to have righteous faith.
Same with Jesus saying "Your faith has saved you." Or to present the timeline, because I credited your faith as righteousness, you will be irrevocably saved. Note, this did not make the person fully righteous, as he or she had not yet been washed with His blood.
Sir, just because something does not make sense to you, does not mean it is not the truth of scripture. No one gets to the Father by imputation, but only by the blood of the Lamb. You can take that to the bank.