Anyone who clearly perceives this may indeed in speaking of the future of any state be wrong in his estimate of the time the process will take, but if his judgement is not tainted by animosity or jealousy, he will very seldom be mistaken as to the stage of growth or decline it has reached, and as to the form into which it will change.
I'm interested in the bolded part. I understand the meaning, but I don't get the syntax. The main verb is διασφάλλοιτο which according to LSJ in the Pass. means "fail of" and takes a gen. But what are we to make of the τὸ and the ποῦ and the ἐστιν? I thought maybe τὸ ποῦ might mean something, but LSJ comes up empty. Any ideas how this works or if some words are implicit?
I don't think it's particularly funky--it's quite a common usage in Greek. I don't have access to my Smyth at the moment (and the online version is too difficult to browse), but I think he has a series of sections on the "free use of the accusative." or something like that, which includes the "accusative of respect." You might look through those sections. (You have to remember that "accusative of respect" is just a category invented by grammarians to collect a large number of passages from Greek authors.) In Greek, this use of the accusative is no more funky that the English prepositional phrase "with respect to," which denotes that the complement has some sort of fuzzy relationship to the clause in which it occurs. Greek does the same thing with the naked accusative. If you've studied Latin, this not a native Latin construction, (except when used in imitation of Greek, particularly in poetry, where it's metrically convenient). In Latin the uses of the various cases are more tied down; Greek is much more flexible.
And then you pile onto that the capacity for Greek to put a neuter article in front of just about anything including questions to create a substantive, and this is the sort of thing you get.
Also, the ability of the genetive to depend on an adverb!
Are you forced to read it that way because διασφάλλοιτο can't take a direct object?
Well, if by "being forced to read τὸ δὲ ποῦ τῆς αὐξήσεως ἕκαστόν ἐστιν ἢ τῆς φθορᾶς ἢ ποῦ μεταστήσεται as an accusative of respect" you mean that there's really no other way to read the sentence, then I would say, yes.
A lot of verbs in LSJ have meanings c. acc. and c.gen and c.dat and ...
The LSJ entry is so short, it seemed another possibility would be to imagine that there was a reading that was c.acc and that the definite article phrase was such an acc. Indeed, you went beyond the LSJ entry in giving an abs. reading of the verb. The only mp reading that LSJ has is c.gen.
I'm not being tendentious. The only things I have strong opinions on grammar-wise are osos and Mastronarde. For everything else, my questions are naive.
Check each of the citations in LSJ and I suspect you'll see that not all of them have genitive complements.
By the way, I've collected some more examples of ὅσον + fem. gen. sing. If you're interested, I'll post them when I have time. These are situations where ὅσον means "how much of," not "how large" or "how many."
Not enough of a sample to conclude that the verb rigorously and invariably takes a genitive complement. After all, LSJ gives "to fail of," "be disappointed of" as translations for διασφάλλομαι, but an English speaker wouldn't insist that those English verbs must be followed by "of" and can't take "with respect to." The accusative of respect is common enough in Greek that it can be used with a wide range of verbs. Think of it as a kind of prepositional phrase without a preposition.
I wouldn't worry about finding a slew of parallels with διασφάλλω: the accusative of respect (or some such free use of the accusative) makes sense here and reads naturally. As you noted, the accusative τὸ δὲ ποῦ . . . μεταστήσεται can't possibly be the direct object of the passive verb διασφάλλοιτο (and nominative τις excludes the possibility that τὸ δὲ ποῦ . . . could be the subject), so how else can τὸ δὲ ποῦ . . . be analyzed, other than as an accusative of respect? Indeed the translation you cited clearly reflects an analysis treating τὸ δὲ ποῦ . . . as an accusative of respect, if my anonymous post on the internet isn't sufficiently authoritative (not that you don't have reason to be wary of anonymous posts on the internet like mine).