If I understand the point of SBC's Thomas Paine quote, it's that while one person can pay another person's financial debt for another, justice does not allow one person to pay a moral debt of another. That is, the justice would allow Jesus to pay my mortgage but not to take my death sentence for me.
It seems to me that the answer involves the required new birth Jesus spoke of to Nicodemus in John 3:3. I believe through that experience God undertakes a spiritual transaction in which the believer is so identified with Christ spiritually before God that what happened to Christ happened to him.
I think Paul was referring to this when he wrote in Galatians 2:19-20: "For through the law I died to the law so that I might live for God. 20 I have been crucified with Christ and I no longer live, but Christ lives in me. The life I live in the body, I live by faith in the Son of God, who loved me and gave himself for me."
Obviously, Christians haven't been physically crucified with Christ, so Paul is discussing a spiritual transaction that has take place.
Similar is Romans 6:4-9: "We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life. 5 If we have been united with him like this in his death, we will certainly also be united with him in his resurrection. 6 For we know that our old self was crucified with him so that the body of sin might be done away with, that we should no longer be slaves to sin-- 7 because anyone who has died has been freed from sin. 8 Now if we died with Christ, we believe that we will also live with him. 9 For we know that since Christ was raised from the dead, he cannot die again; death no longer has mastery over him. 10 The death he died, he died to sin once for all; but the life he lives, he lives to God. 11 In the same way, count yourselves dead to sin but alive to God in Christ Jesus."
Also, Colossians 3:1-3: "Since, then, you have been raised with Christ, set your hearts on things above, where Christ is seated at the right hand of God. 2 Set your minds on things above, not on earthly things. 3 For you died, and your life is now hidden with Christ in God."