I'm trying to not define what is moral or good here, but am really
focused on the process of "redemption" from one to the other: if it's
possible, and how would it occur?
Yes, it is possible, it can occur, for example through the State: Prostitutes, pimps, blackmailers, thieves, gangsters, must pay taxes. For the State, "Pecunia non olet", "money does not stink".
The crack tax which was passed by the Tennessee General Assembly in January 2005, levies on illegal drugs like moonshine, cocaine, and marijuana. It is up to drug dealers to pay at the state revenue office, and then they receive as stamp to provide evidence that they have paid.
The "claim of right doctrine" in the United States, which is to hold that illegal proceeds could not constitute income because the taxpayer has no claim of right to the income and is under an obligation to return the proceeds. This doctrine was rejected by the United States Supreme Court in 1961 in favor of an "economic benefits approach", which asks the question whether the taxpayer "'has such control over an ill-gotten gain that, as a practical matter, he derives readily realizable economic value from it'". The rejection of the "claim of right doctrine" was based on a clearly-delineated policy decision by the Supreme Court:
"We should not continue to confound confusion, particularly when the result would be to perpetuate the injustice of relieving embezzlers of the duty of paying income taxes on the money they enrich themselves with through theft while honest people pay their taxes on every conceivable type of income."
In addition, "the purpose of Congress was to use the full measure of its taxing power".
The courts in the United Kingdom have reached a level of clarity: proceeds will be taxed as long as they arise or accrue from a trade, whether legal or illegal. This standpoint appears to be underscored by a move away from the idea that the State, by taxing illegal proceeds, condones the activity from which these proceeds spring, to the idea that the State should not allow the wrongdoer to benefit from advantages which are denied to the honest taxpayer.
In England, various courts have repeatedly rejected the argument that a trade ceases to be a trade for the purposes of the Taxes Acts because it is illegal. The reason why they have said that profits of burglary are not taxable is not because burglary is illegal but because burglary is not a trade. Conversely, if the activity is a trade, it is irrelevant for taxation purposes that it is illegal. It is not necessary to reach any conclusion as to whether profits from an illegal trade are assessable to income tax under the present law of England. There may be lawful trade, there may be unlawful trade. But it is still trade.