Tugodum, do you know the American idiom “Declare victory and get out”? 
I’m running out of time, my friend. I have to go perform more mundane tasks, like washing dishes, mowing the lawn, weeding the garden, etc.. I’ve enjoyed our little chat and hope that sharing my views on the question will perhaps give you something else to consider as you gain an understanding of this particular construction.
Wow… this is really running in circles. I repeat what I said at the beginning of my post: “I think you’re getting hung up on whether you should translate the internal object into English with an adverb.” If you want to understand this grammatical construction, I suggest focusing on the Greek grammar in that post, or the descriptions you received in the Apology thread, or (again) just about any Greek grammar (perhaps one not in English?). But that’s enough from me.
Thanks everybody. I see now from a number of reactions that translation is off-topic on this forum. Learning Greek does not include learning how to translate Greek. I will keep this in mind.
I sure do. I also see that the use of either of them differs from language to language.
I meant in Greek, as between μεγαλα αμαρτειν and μεγαλως αμαρτειν, for instance. But never mind.
mwh, but this is a very subtle difference! I had been seeing it vaguely before, I am seeing it a bit clearer after this discussion, but to really “see” the difference" for me means to be able to define it. I am not yet there. Are you?
p.s.
I was assuming you meant a difference in meaning. The grammatical one I can define all right.
p.p.s
The knowledge of the sheer fact that there is a difference (which I never doubted) is, in my view, useless unless one knows, also, what the difference is.
I don’t see how this discussion could have gotten anywhere in the first place without copious Greek examples, or by bringing in other sources. There is no way to reason oneself into being a better translating.
Anyway, I think that this may interest Tugodum: https://books.google.com/books?id=d-UIAQAAMAAJ
If you can’t read German, of if you can only half-read it like me, you may still find the Greek examples useful.
Thanks a lot, Joel!
If you come across anything on the difference in meaning between locutions like μεγαλα αμαρτειν and μεγαλως αμαρτειν, this will be highly appreciated too!
Well, Kühner makes some references to the adverbial character of that sort of usage here, but I’m don’t see (after a quick scan) that he makes any absolute prescriptions:
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0020%3Asmythp%3D410
I don’t see there any comparison between such usage of accusatives and the use of adverbs (which is what I am interested in).
You’ll have to make your own investigation of that, I think. But the examples in Anmerk 5. are pretty useful. For example, “θυγάτηρ ἄνανδρος πολιὰ παρθενεύεται” from Helen. I don’t think that a good translation of that into English would use adverbs.
35 a5: θαυμασία…ἐργαζομένους
Burnet’s note ad loc.: ‘going on in an extraordinary way’