Your theory does not accords with "there shall be joy before the angels of God upon one sinner doing penance" that follows the discourse of lost sheep in Luke 15, and precedes the parable of the Prodigal Son. The recovery of the sheep is through penance. The Prodigal son parable elaborates on that.
" The recovery of the sheep is through penance"
The word is repent (to change one's mind for better, heartily to amend with abhorrence of one's past sins) Luke 15:7, "I say unto you, that likewise joy shall be in heaven over one sinner that repenteth, more than over ninety and nine just persons, which need no repentance." It does not carry the idea of penance but a change of the will.
The prodigal son is just an elaboration of that. It was not the sons feeling sorry or doing anything to earn the father's disposition towards him, just his coming home, "he was lost, now he's found".Luke 15:22-24, "But the father said to his servants, Bring forth the best robe, and put it on him; and put a ring on his hand, and shoes on his feet:
And bring hither the fatted calf, and kill it; and let us eat, and be merry: For this my son was dead, and is alive again; he was lost, and is found. And they began to be merry."
Notice the Greek conjunction "but" that limits what the son is doing and changes the emphasis of the parable to what the father is doing. He could care less what the son is saying or doing, just that "my son was dead, and is alive again; he was lost, and is found". For that, there is joy in the house.