Your assumptions are not just unrealistic, they do not appear to be self-consistent, which is much worse.
"Crime is the breach of rules or laws for which some governing authority (via mechanisms such as legal systems) can ultimately prescribe a conviction." If you abolish punishment, you abolish crime, however silly it sounds. There is no longer a distinction between immoral and illegal. The "crime rate" would be trivially zero. The "moral offense" rate would be hard to calculate without restoring some gradation of immorality, otherwise being rude to a person has the same weight as killing them.
I see no way to create this gradation other than by assigning different punishment to different offenses, in which case we are back to where we started.
A more consistent model would be "what if there is a maximum level of punishment beyond which there is not further reduction in crime rates, and this level is entirely too low to the victim's liking?" When stated this way, the answer is obvious: most people would adjust their expectation of a just punishment to fit that prescribed by the law. This has happened over the ages in nearly every society already (the adjustment, not the punishment optimization), in one direction or another.
For example, capital punishment used to be dispensed rather freely not that long ago. On the other hand, swindling was not a crime until rather recently, and often still isn't. Societies adjust to what the law says, and change the law when there is enough support, however imperfectly.
Given this self-adjustment of expectations of a just punishment, all that remains from your question is "how to find the optimal level of punishment for a given offense?" A zero-punishment offense would be considered an immoral act, all the rest would be forms of infractions/civil offences/crimes.
Least convenient possible word: define "crime" as that which is punished by present laws. Or use another, punishment-independent, definition (enumeration). Or, allow zero penalty to be included in the criminal code, so crime would still be technically forbidden, but the punishment for any crime would be no action.
Here is a thought experiment for you. There will be some bold assumptions here, and they may be regarded unrealistic. I am aware of that and the purpose of this query is not to propose some truths about society in general, but to isolate certain characteristics of preferences regarding the societal institutions of law enforcement and punishment.
Assume that there existed a highly trustworthy model that showed beyond reasonable doubt that crime rates anti-correlated with harshness of punishments imposed on criminals. So basically, if policies changed towards shorter sentences, lower fines and lighter penalties, the number of criminal acts decreased (in every category).
Further assume that this was empirically tested and each time penalties went down, fewer and fewer crimes was committed. But the dependence was not linear so if we would get rid of punishments all together - there would still be murders, rapes, robberies etc. But, the crime rates would be minimized in that case. To summarize: We knew that crime rates would be at minimum if there was no consequences at all.
With no penalties, somebody could simply kill or rape your mother, sister or child and move in next door and live a nice and happy life in front of your very eyes, without society doing anything about it! Bare in mind now that this is the situation where the probability of your mother, sister or child being abused, robbed or killed is minimized!
Would it be reasonable to go trough with this demobilization that would spare lots of innocent people all the pain of getting robbed and abused, given that those criminals still out there can do anything they want and go free?