Here is the hierarchy of apologies, their function and their motivation, 1-11, from most admirable to despicable: 
1. An apology motivated by the realization that one’s past conduct was unjust, unfair, and wrong, constituting an unequivocal admission of wrongdoing as well as regret, remorse and contrition, as part of a sincere effort to make amends and seek forgiveness.
2. An apology motivated by the realization that one’s legitimate and defensible action or words caused unanticipated, excessive, or unnecessary harm to a particular party or parties. The apology expresses a sincere regret that the harm occurred.
3. An apology motivated by a desire to accept accountability for an event or occurrence that one may not have caused, but was responsible for in some way.
4. A spontaneous apology intended to demonstrate compassion and sympathy for the victim or victims of the unavoidable consequences of a necessary action.
5. A spontaneous apology designed to prevent future, preventable harm by expressing regret that a past action was necessary or that it occurred at all.
6. A forced or compelled version of 1-4, when the individual (or organization) apologizing knows that an apology is appropriate but would have avoided making one if he or she could have gotten away with it.
7. A forced or compelled version of 1-4, in which the individual (or organization) apologizing may not sincerely believe that an apology is appropriate, but chooses to show the victim or victims of the act inspiring it that the individual responsible is humbling himself and being forced to admit wrongdoing by the society, the culture, legal authority, or an organization or group that the individual’s actions reflect upon or represent .
8. A forced apology for a rightful or legitimate act, in capitulation to bullying, fear, threats, desperation or other coercion.
9. Deceitful apologies, in which the wording of the apology is crafted to appear apologetic when it is not (“if my words offended, I am sorry”). Another variation: apologizing for a tangential matter other than the act or words that warranted an apology.
10. An insincere and dishonest apology designed to allow the wrongdoer to escape accountability cheaply, and to deceive his or her victims into forgiveness and trust, so they are vulnerable to future wrongdoing.
11. The Impossible Apology: An inherently unbelievable apology for conduct or words so unethical and so extreme that nobody could possibly say or engage it accidentally or unintentionally. Such an apology for words or conduct of signature significance, indicating that the speaker or wrongdoer is unethical and untrustworthy because no individual who is ethical and trustworthy would behave in such a manner even once, is not merely cynical and a travesty, but insulting to its intended audience.
Ethics Alarms 
Is this your own formulation from start to finish? Or did you develop this list after considering other philosopher’s own descriptions and understandings of apologies?
Mine, entirely.
How is #2 lesser in value than #1? I think they’re about the same.
It seems that if you are apologizing in #2 for something you legitimately in the right doing…the apology isn’t *actually* necessary for the original conduct. If, as part of a larger and defensible series of conduct, a component of your conduct harms others unintentionally, then it seems that the apology here should be seen as an apology for a distinct action.
AND, IF, that apology must be couched inside a larger explanation of *justifiable action*, apologizing for it is actually *more* exemplary than a mere level 1 apology.
BUT, IF, that apology is made as though the individual action inside the larger justifiable action is separated from that action, then that apology should be evaluated on its own merits…meaning that a #2 apology would never occur.
Since I tend to lean towards the latter…I don’t think I understand your #2.
The key thing that throws me off, is both require “sincere regret for harm occurred”. That some conduct is standalone and other conduct may have been a component or a larger ethically justifiable behavior pattern shouldn’t make a difference.
A soldier in war who vandalizes a private residence by callously and purposelessly throwing a hand grenade in the house has done wrong. Let’s say he was a young and angry man in stressful situation and lashes out. Only to recognize the real harm he has done and sincerely apologizes to the home owner and does what he can to repair the damage.
A different soldier in war, has to take out a machine gun nest in a back alley, and in throwing the hand grenade towards the machine gun nest, misses and it goes into a private residence and destroys the living room. After the battle, this young soldier sincerely apologizes to the home owner.
Soldier 1 has given a #1 apology in your book.
Soldier 2 has given a #2 apology in your book.
How is soldier 2’s apology a lower rank than soldier 1’s?
Likewise, #3 seems to be an individual taking on even *more* than they are actually responsible for. How does this lower the value of the apology? Or is it lower in value because the individual is really not apologizing at all…?
I guess I get confused because there are two different apologies in this list of 10-
1) An apology for *actual harmful conduct* ranked on two continua – one of sincerity and willingness to actually be held accountable and the other one of how actually accountable the apologist is.
2) An apology for conduct *not* actually harmful, in which a great deal of contrived harm by a miscreant self-styled victim, seeks from an accused individual – ranked on just how the push-over accused goes about the “apology”.
Indeed. All still apologies, though, so both types are on the list.
The relative rankings are only generally accurate. #2 gets ranked lower than #1 only because #1 requires more than #2. #2 is the best apology someone in that circumstance can make, but it mostly requires accountability and empathy.
Because #1 is acknowledging wrongdoing and making amends. #2 is apologizing for bad moral luck. It’s nice, but it’s just not as much of a sacrifice or demonstration of character and contrition.
Is there an ethical obligation to “make amends” for unanticipated harm resulting from otherwise justifiable action?
Nope. There’s no obligation to apologize, either.