> * 真 makoto, a word often glossed as "sincere" but not identical in meaning: it's about the amount of effort you're willing to take on, not how "honestly" you feel something
While it's true that makoto can be translated as sincere(ly) in constructions like "makotoni moushiwakearimasen" (I sincerely apologize) (although this is written 誠に rather than 真に), it is unlikely that the word makoto would be used in a phrase like "a sincere apology" or in discussing how sincere an apology was, so I don't really think introducing the word "makoto" in your comment sheds any additional light on japanese culture surrounding apologies.
You could actually make the exact same comment about how "real" in English can also effectively mean sincere in "really sorry" and draw the same conclusions about American culture.