Wolf, let me try two more comparisons.
1- Paul has 2 brothers. His parents have left a large inheritance to all their children, and Paul doesn’t want to share. He kills his brothers, and legally inherits all the money (legally inherits, because he is never charged with the deaths).
He has the money legitimately, but came by it in the wrong manner. In this case, charata on the murders would probably be insufficient- the money he has is tainted. I would probably agree that he should burn/give away the money to be a true penitant.
2- James is looking for work as a mechanic. He has no experience and no training, so he makes up experience on his resume and bluffs through interviews. But James has some natural talent for working with cars and is never found out, his work is just as good as any reputable mechanic. After a year on the job, he wants to do tshuva for the manner in which he got the job.
He apologizes to his boss for lying his way in. But he does not regret the good work he has done, nor does he wish to lose his job. He just wishes that he had gotten the job without lying, i.e. either that he had been able to get the training and experience to apply honestly, or that he had told the truth and gotten the job anyway.
Your situation is akin to #2. If you think it is akin to #1 then I disagree with your assessment.