You have come VERY close to the kingdom of God. Your interpretation lacks only a very small observation.
I used to read this parable and identify the characters as most do:
I am the widow
God is the unjust judge (what a characterization!)
Try this one on for size and see if it doesn't fit a little better:
I am the widow AND the unjust judge. After the parable Jesus tells us that God answers our prayers "speedily" (KJV) or "quickly" (NIV). That would eliminate God as the unjust judge character who got tired of this woman banging on him day and night.
God answers every prayer quickly and speedily but because of the condition of our hearts a lot of times, we are unwilling to receive the graces (gifts) that He has provided. Many times we cannot bring ourselves to the place where we actually believe in His goodness we limit our lives to whatever we ourselves can achieve.
The unjust judge is our own hearts. We do not receive anything from God except it be by faith. (For we are saved by grace through faith). If my heart cannot bring itself to the belief that God wants to bless me then I cannot receive what I cannot believe.
God answers all pray quickly. "For no matter how many promises God has made, they are 'Yes' in Christ" (2 Cor. 1:20). If we are in Christ then all promises to us are "Yes". Please be cautioned, however, persecution is as much a promise from God as "whatever you wish" (John 15:7).
The heart must be persuaded. "Abraham believed God and it was imputed to him for righteousness". As the apostle Paul points out, this was no casual mental ascent to the existence of God; it was a belief in what God promised. And that is what counted as righteousness.
"He staggered not at the promise of God through unbelief but was strong in faith giving glory to God; and being fully persuaded that what God had promised, he was able also to perform." (Rom. 4:20-21)
Abraham had to fully persuade his heart (the unjust judge) that God's promise was "Yes". And about 25-years later, Isaac was born. Sometimes, the persuasion process takes a little while but it's not God we are persuading, it's our own unjust and unbelieving hearts.
Or so it seems to me.