Did King David know about imputed righteousness?

A common Reformed doctrine is the view that a man is justified by God imputing (considering by merely declaring) a man righteous. He will not make the wicked man righteous, the man might still not be capable of doing anything good beyond faith, but God will pretend the man is righteousness nonetheless by cloaking the sinner He selected with the righteousness of Christ. Essentially creating a white washed sepulcher of a saint.

To support this concept of imputed righteousness many point to Romans 4:7-8

“Blessed are those whose transgressions are forgiven, whose sins are covered. Blessed is the one whose sin the Lord will never count against them.”--Romans 4:7-8

It is supposed that because a man's sins are not 'counted against', or 'imputed to him' it means righteousness was imputed instead. This is important since this is quote the Old Testament, which would suggest justification in the Old Testament was similar to, if not the same as, in the New Testament.

Romans 4:7-8 is quoting Psalm 32:1-2:

 Blessed is the one
whose transgressions are forgiven,
    whose sins are covered.
Blessed is the one
    whose sin the Lord does not count against them
    and in whose spirit is no deceit.--Psalm 32:1-2

This was in reference to the sin with Bathsheba

Then David said to Nathan, “I have sinned against the Lord.” 

Nathan replied, “The Lord has taken away your sin. You are not going to die. But because by doing this you have shown utter contempt for the Lord, the son born to you will die.”-- 2 Samuel 12:13-14

Some Protestants will point to the wording here. David is not directly begging for forgiveness, he does not say "forgive me, Lord" but instead "I have sinned against the LORD," they then claim the grammar implies David was forgiven before he repented which is why Nathan said, "The Lord has taken away your sin." They say 'has' means the LORD did it before the incident (possibly even from the minute he was regenerated). Though, it is much more likely Nathan was saying God forgave David the moment he acknowledged his sin, which was just then in the past by seconds to the time Nathan said God "has taken away your sin."

If this be the case that David had his sin forgiven from the time he was regenerate, long before the affair Bathsheba, and David is told about imputed righteousness, then why does David beg for forgiveness from the LORD much later for the census:

And David said unto the LORD: 'I have sinned greatly in what I have done; but now, O LORD, put away, I beseech You, the iniquity* of Your servant; for I have done very foolishly.'--2 Samuel 24:10 

*Some may object by using translations that read 'guilt' instead of 'iniquity', it is actually עֲוֺן  'avon which is usually translated "iniquity"--a major sin. In fact, the verse the doctrine revolves around Romans 4:8 is quoting Psalm 32:2 which uses the same exact word--עֲוֺן  'avon. Yet, we see in 2 Samuel 24:10, King David has to ask God to remove his 'avon.

Let's compare verses:

And David said to the LORD: 'I have sinned greatly in what I have done; but now, O LORD, put away, I beg You, the iniquity [עֲוֺן 'avon] of Your servant; for I have done very foolishly.' --2 Samuel 24:10

וַיֹּאמֶר דָּוִד אֶל-יְהוָה, חָטָאתִי מְאֹד אֲשֶׁר עָשִׂיתִי, וְעַתָּה יְהוָה הַעֲבֶר-נָא אֶת-עֲוֺן עַבְדְּךָ, כִּי נִסְכַּלְתִּי מְאֹד. 

with:

Happy is the man unto whom the LORD counts not iniquity [עָוֺן 'avon], and in whose spirit there is no guile.--Psalm 32:2

 אַשְׁרֵי אָדָם--לֹא יַחְשֹׁב יְהוָה לוֹ עָוֺן;    וְאֵין בְּרוּחוֹ רְמִיָּה

and again,

And David spoke to the LORD when he saw the angel that smote the people, and said: 'Lo, I have sinned, and I have done iniquitously; but these sheep, what have they done? let Your hand, I pray You, be against me, and against my father's house.'--2 Samuel 24:17

also repeated in

 And David said to God, I have sinned greatly, because I have done this thing: but now, I beg You, do away the iniquity of Your servant; for I have done very foolishly.--1 Chronicles 21:8

 "I beg you, take away the guilt"--this does not sound like the words of a man that knew about imputed righteousness. David begged God to only punish him and his family, not the entire nation. Was David asking God to impute sin to him and his own family by the Reformed's reasoning?  The fact that David begged for forgiveness makes it clear he believed God did impute the sin to him for the period of time he was impenitent.

Let us also compare the words used to expression forgiveness used in 2 Samuel 12 vs 2 Samuel 24's episode, we see the word "put away" or "pass" is used in both.

And David said unto Nathan: 'I have sinned against the LORD.'  And Nathan said unto David: 'The LORD also hath put away [הֶעֱבִיר he'evir] thy sin; thou shalt not die. --2 Samuel 12:13 

וַיֹּאמֶר דָּוִד אֶל-נָתָן, חָטָאתִי לַיהוָה;  וַיֹּאמֶר נָתָן אֶל-דָּוִד, גַּם-יְהוָה הֶעֱבִיר חַטָּאתְךָ--לֹא תָמוּת. 

Now see the word used in 2 Samuel 24:10:

And David said unto the LORD: 'I have sinned greatly in what I have done; but now, O LORD, put away [הַעֲבֶר ha'aver], I beseech Thee, the iniquity of Thy servant; for I have done very foolishly.' --2 Samuel 24:10 

וַיֹּאמֶר דָּוִד אֶל-יְהוָה, חָטָאתִי מְאֹד אֲשֶׁר עָשִׂיתִי, וְעַתָּה יְהוָה הַעֲבֶר-נָא אֶת-עֲוֺן עַבְדְּךָ, כִּי נִסְכַּלְתִּי מְאֹד.

Both are H5674 in Strong's Concordance (note a concordance is not a lexicon) just used in different forms.

2 Samuel 24 and 2 Samuel 12 both use the same word but in use chapter 12 to inform David he as been forgiven, and chapter 24 to beg God to forgive David. Since 2 Samuel 12 is being commented on by Psalm 32, which is about not imputing iniquity, forgiving sins, etc. it would follow even more so that David did not believe he was permanently justified/forgiven before God irrespective of his conduct.

It is pretty obvious David is saying God did not count his iniquity once David confessed his sin. This is made even more obvious reading the rest of the Psalm:

When I kept silence, my bones wore away through my groaning all the day long. For day and night Your hand was heavy upon me;  my sap was turned as in the droughts of summer. Selah I acknowledged my sin unto You, and my iniquity have I not hid; I said: 'I will make confession concerning my transgressions to the LORD'-- and You, You forgave the iniquity of my sin. Selah--Psalm 32:3-5

He was silent...that David did not confess his sin, so he groaned about his condition.

The hand of the Lord was heavy--God pushing him to repent for his sin against God.

I acknowledged my sin......I will make confession concerning my transgressions...and Thou forgavest the iniquity of my sin"....That is to say--David sinned, David repented, and God took away David's iniquity at this point.

It is clear that David was not "imputed" with his sin as a result of his confession of the sin, not because he was already forgiven a long time in advance. King David who some suppose taught imputed righteousness, sure seemed to lack confidence in his security of salvation due to his moral failings. David certainly was not Luther who believed in a Christian as being simultaneously being a saint and a sinner.

However, when you string together a system based in part on the unbiblical doctrine of Penal Substitutionary Atonement, such hoop jumping becomes routine, necessary, and inevitable.