So, this makes me want to know your view of a few of the core points:
1. Isn't calling Socrates' sacrifices "self-indulgence" if done for virtue alone the same as joining the critics of virtue ethics who routinely say that "Stoic love isn't really love, because pursuing virtue is self-centered, whereas love is self-sacrificing?" And if so, isn't the standard rebuttal to your argument to point out that in Stoicism (and indeed Socrates), the distinction between selfishness and selflessness is blurred, because they really do truly believe that we help ourselves by helping others and vice versa? Am I to understand that you find this framing of Socratic/Stoic justice unsatisfying?
2. You list "winning," entertaining "spectators," and your own "satisfaction" as reason to "play the game." But I've always found Cicero's discussion of self-sacrifice in battle to be an interesting test of the ultimate good: if a soldier sacrificing themselves in battle for the sake of virtue dies so quickly that they never have any chance to feel a sense of "satisfaction" at their own bravery—have they achieved the ultimate good, or missed out on it? It seems to me the Stoics would say yes—but you might have committed yourself to saying no, since auxiliary enjoyments like "satisfaction" are dependent on fortune, and may or may not result from a brave action.
3. Yes, external interaction with the world is fundamental to the Stoic conception of virtue (without preferred indifferents, Cicero argues repeatedly, virtue is vacuous). And yes, we come to value virtue initially through those things—personally, of the Stoic arguments for virtue as the ultimate good, I've always been most impressed by the "satisfaction" I feel when hearing stories of great people. As Seneca argues in Letter 120, that ability to recognize virtue (and perhaps feel satisfied by it and desire it?) is the basis of Stoicism. But just because we come to recognize virtue through a kind of satisfaction doesn't mean we stop there. Does your view of virtue leave any room for the idea of a sort of oikeiōsis whereby even if we initially approach virtue for other reasons, we come (like the self-sacrificing soldier) to value it for its own sake, above and over those external things?