How can God justify the ungodly [Romans 4:5] and still maintain His integrity to His holy law which condemns sinners [Galatians 3:10]? I ask this because the law of God clearly prohibits an innocent man dying for the guilty:
Ez 18:20....
I think I understand what you're getting at. If so, I agree, your question has not been answered (at least to the point I started drafting this response!). However...
First, I think you have slightly misconstrued the Ezekiel passage, "the law of God clearly prohibits an innocent man dying for the guilty." That's a bit of a narrow and wooden interpretation, and seems to disregard the immediate context.
The context of the whole chapter clearly shows that God is speaking about humans. The proverb quoted in verse 2 is not part of the biblical Proverbs; it is a saying of man, which seems to implicate God as a wrongful judge of men, who suffer for the sins of their parents. God is explaining, through Ezekiel, that He does not judge men in this way. He emphasizes His own righteous judgement, and calls all men to repent of their own sins.
Second, I think the way you put it, "clearly prohibits an innocent man dying for the guilty", is simply incorrect. This passage does not actually "prohibit" an innocent man dying for the guilty (either 'on behalf of' or 'in place of'). That phrase, and meaning, just are not there. Again, the passage is declaring that God's judgement is righteous, against man's claims that it isn't (v. 25).
I believe your question is a good one, in that you see something which doesn't make sense to you, and you're willing to ask hard questions about it. Kudos for that. I also believe that, as asked, there isn't an adequate answer for your question, because it is founded on a wrong interpretation of the Ezekiel passage.
I have found that the more my beliefs about God line up with Who He actually is, the more clearly I see Him. For example, I am convinced that God is good, so even though some scriptural passages make God look nasty, I try to look beyond the surface and see how God is actually being good, sometimes in "higher ways" (Isaiah 55:9).