FWIW the Greek just says "short-lived," and doesn't have any connotations of "effects beyond themselves." The word used is ὀλιγοχρόνιος, which is a compound of ὀλίγος (few in number) and χρόνος (time). If you like Meditations, I think it's also worth reading what Nietzsche has to say about the Stoics for a little contrary perspective.
This is one of the things about translations. While it’s wonderful to have access to perspectives from across cultures and times, it can be difficult to know if you are getting a correct reading if you’re not able to work in the original language. That’s one of the nice things about having the two versions, I can use them to clarify against each other sometimes.
There may be some overlap in placed, but he has some pretty sharp criticism for them in Beyond Good and Evil:In truth, the matter is altogether different: while you pretend rapturously to read the canon of your law in nature, you want something opposite, you strange actors and self-deceivers! Your pride wants to impose your morality, your ideal, on nature--even on nature--and incorporate them in her; you demand that she should be nature "according to the Stoa," and you would like all existence to exist only after your own image--as an immense eternal glorification and generalization of Stoicism. For all your love of truth, you have forced yourself so long, so persistently, so rigidly-hypnotically to see nature the wrong way, namely Stoically, that you are no longer able to see her differently. And some abysmal arrogance finally still inspires you with the insane hope that because you know how to tyrannize yourself--Stoicism is self-tyranny--nature, too, lets herself be tyrannized: is not the Stoic--a piece of nature?
Sure, but he's not criticizing stoic ethics there, he's doing the same thing he did when he pointed out that Socrates was ugly. Nietzsche was after an ethics without some external grounding, because god was dead and there was nothing that could serve as a ground, so he criticized the foundations of ethical systems of the past, but that didn't stop him from rolling with the parts he liked. If there can be no foundation for any ethics, knocking the stool out from under one doesn't make it less valid than any other.
Yeah, but again that's why I said he ended up getting to the same place(s), but my point was that he didn't get there because of the Stoics.