We need to keep in mind that this was not written to the United States of America but to the kingdom of Israel under Solomon. "My people" were the Israelites and their wicked ways and idolatry are recorded in Scripture. It would appear that this promise was never fulfilled for Israel and instead the ten tribes went into Assyrian captivity and the kingdom of Judah went into Babylonian captivity followed by other captivities. However, there can be a general application for Christians in any country to pray for the healing of their country by firstly turning away from all false doctrines and practices within Christendom.
From what you have written above, and I have quoted, it seems to me that the "saints of the Church" needs to humble themselves and repent of their sins.
As for your gracious understanding of God's purposes for the Israelites, the iniquities of the fathers would put a barrier between God and the Israelites for four ages, i.e. a little longer than 4,000 years from the time of Isaac's birth until the full period of this separation of Israel from God has run its course to completion.
Within the next 22 or so years when the end of the four age of the visitation of the iniquities of Israelites is completed, God does require the Israelites of the conclusion of the visitation time to humble themselves and repent of their fathers iniquities of continual idolatrous worship as well as their own iniquities of continual idolatrous worship during the third and fourth age of their existence from the time of the birth of Isaac.
In our near future, the kings of the earth will gather at Armageddon and God will judge them for the tribulation that they heaped upon Israelite peoples scattered around the earth in all of the nations.
The Christian Church needs to stop its continual idolatrous worship just as much as the Israelites need to. To say that our sins are covered by the Blood of Christ on the Cross is to make a mockery of Christ's sacrifice for all the people of the earth. We lead ourselves astray if we think that we have no sins that need repentance of. The Church as well as the political systems in many countries have played at being God thinking that they can "fix" the problems the people of the earth face by tweaking here a little, there a little and the control balances of the earth will be "FIXED."
That is turning away from God. That is acting God like. That is what I call idolatrous worship where we have replace God in our lives and begun to act God like.
My sins are great in the eyes of the Lord as I try to control my life so that I will have eternal life, after the final judgement, but the truth of the matter is, as Christ taught, that those who try to save their own lives will become the candidates who will be dispatched into the Lake of Fire, which is the Second Death, at the time of the Final Judgement.
Am I righteous? I am sure that I do not measure up as I think I might do. I fall short of His requirements of being His disciple.
Are you, righteous? From what you have written, I do not believe that your theological constructs comes anywhere near what God requires of us.
My heart cries out to God for His help. I see God's Hand working to draw me into His loving embrace. I have to let God Hold my hand instead of me trying to hold onto God's hand. That requires great faith on my part that the God that I worship is sufficient to provide for all of my needs, in this life and in the Next.
Shalom