Excellent concept, David. First, let me offer some minor corrections to your text: This is based on my assumption that with this particular exercise (unlike a lateral paraphrase) you want the syntax, anyway, to be as close as possible to the original.
ἐν μὲν οὖν τῷ πρώτῳ χρόνῳ, ὦ πιστεύοντες, (1) πάντων (2) ἦν βιαιότατος: καὶ γὰρ στρατηγὸς δεινὸς καὶ τραχὺς καὶ σχετλιῶς τοὺς πολεμίους ἀναιρῶν: (3) ἐπειδὴ δὲ τὸ (4) αἷμα κατήχησε τοὺς λόφους τοὺς Δαυλιας, πάντων τῶν καλῶν ῥεῦσαν (5) αἴτιον (5) ἡμὶν γεγένηται.
1. plural in the original.
2. needs to be switched to masculine because Asoka was a man.
3. I think the participle should be retained.
4. The original has the article.
5. needs to be neuter agreeing with αἷμα.
Doing this does seem to work in that you have to get far more up and personal with the syntax than just translating.
Well, yes, from my perspective, it is better than translation because you don't have to leave the target language, and yes, it forces you to pay very close attention to the syntax without betraying it by putting it into meta-language terms. Rather, one is ENGAGING the syntax by substituting vocabulary and giving it your own meaning. The exercise is ACTIVE, which is good, and yet by retaining the syntactic skeleton you are working with and further internalizing real, presumably proper Greek, especially in the tricky area of word order and how sentences are constructed/linked. By choosing the original passage, and by choosing the meaning of your version, you can write about something which interests you, (as opposed the tedium of English-to Greek exercises) which SLA experts say is always an effective learning strategy.
Now, we must acknowledge that in switching the vocab (and the meaning!) we of course may well wind up producing something that would not sound quite right to native Ancient Greek ears. This is also a danger with paraphrase. But I think the pay-off is worth it. When you make the vocabulary switch, you will probably have to look up words and forms, which I think is a good thing, if you turn around and use that to actively produce the language. With this method, like the lateral paraphrase, you take real Greek and then cut-paste-adapt. This is less tedious, maybe, than starting from scratch, and again is grounded in real Greek. Your method reminds me of something Paul Nitz once said, that to really get something out of the Greek you read, you have to DO something with it.
We have to come up with a name for this method, the basic idea of which I think I had thought of before but never quite tried. It is close to what they call "semantic switch-outs," but there you change things like the tenses and persons to give practice for the forms.. Here, presumably, all the grammar remains the same, but the vocab is changed. Maybe we should call it "vocab switch-outs" or "syntactic skeletons."
Here is my own attempt at using your method. It does not change the original as much as yours, but I think it accomplishes the same pedagogical goal. The subject of the first two sentences is Lucifer:
ἐν μὲν οὖν τῷ πρώτῳ χρόνῳ, ὦ φίλοι, πάντων ἦν ἄριστος: καὶ γὰρ ἄγγελος καλὸς καὶ ὑπακουὸς καὶ καλῶς κατὰ πάντα δουλεύων: ἐπειδὴ δέ ἡ ὑπερηφανία ἐφάνη, πάντων τῶν κακῶν φανεῖσα αἰτία μοι γεγένηται.
I think you have picked a good sentence, because while the syntax is not overly complicated, it is representative of the type of the syntactic skeletons that English speakers need to not just read but somehow drive deeper into the hardwiring of their brains. It's also a nice piece of rhetoric.
You should try it with another few sentences. I will try to do the same.