"Your proposed English translation represents a different understanding of the Greek syntax than what you seem to be arguing for".
That could be true. In German the suggestions was (normal Syntax, "dazu" is a correlate of εις ο for the infinitive extension):
"Jedenfalls sind wir dazu gelangt, demselben Maßstab zu folgen, derselben Gesinnung zu sein".
English (another try):
"In any case, to that/it we have come, to follow the same standard, to be the same mindset".
Assuming the prepositional phrase directing to the right.
I know that the BDR idea is realized in all the version and all versions treat this as adhortatives. The examples at least showed me, that such is never made. That caused the hesitation.
"is combined with the verbal notion of an infinitive to get a meaning something like "began to."
Yes, but not only this, as Verbs as "arrive, come to" have (see at least the NT examples, I named), such extensions with an infinitive.
"As far as I know, φθάνω is never used with an infinitive in the way you seem to think".
Yes, e.g. this one: 1Kings 12.18: „καὶ ὁ βασιλεὺς Ροβοαμ ἔφθασεν ἀναβῆναι τοῦ φυγεῖν εἰς Ιερουσαλημ“.
"we have a "point of arrival" specified by εις ο which completes the predication of the verb φθἀνω"
Of course, sometimes, but not if treated as correlate, pointing to the left or right, granting the extension before or after.
"To get around this you would seem to have to come up with a novel explanation for the otherwise normal function of εἰς ὄ"
Pointing to the left or to the right as correlate is not so novel for εἰς ὄ.
If it is too unreasonable or uncommon for you, we could leave it as it is, at least for me the case is not settled, but who am I to propose something all other version are all against it
![Smile :-)](./images/smilies/icon_e_smile.gif)
P.
P.S. Philip 4.2 would be another example of an usual expansion of a main verb (predicate), already discredited here, by a depending infinitive (here without correlate): Εὐοδίαν παρακαλῶ, καὶ Συντύχην παρακαλῶ, τὸ αὐτὸ φρονεῖν ἐν κυρίῳ.