Doesn't seem to be a syntax issue. Peter has: τὸ τοῦ θεοῦ πνεῦμα
What we do find is ὁ λόγος τοῦ θεοῦ1Pet. 4:14 εἰ ὀνειδίζεσθε ἐν ὀνόματι Χριστοῦ, μακάριοι, ὅτι τὸ τῆς δόξης καὶ τὸ τοῦ θεοῦ πνεῦμα ἐφ᾿ ὑμᾶς ἀναπαύεται.
In Patristic texts we find frequent use of ὁ τοῦ θεοῦ λόγος with and without conjunctions.Rev. 19:13 καὶ περιβεβλημένος ἱμάτιον βεβαμμένον αἵματι, καὶ κέκληται τὸ ὄνομα αὐτοῦ ὁ λόγος τοῦ θεοῦ.
ὁ τοῦ Θεοῦ Λόγος used by almost everyone 500+ occurrences.
Cyrillus Thesaurus de sancta consubstantiali trinitate
75, p400, l 12
Ἄνθρωπος γέγονεν ὁ τοῦ Θεοῦ Λόγος, οὐχ ἵνα πά-
λιν ὡς Θεὸς πρὸ τῆς ἐνανθρωπήσεως πάντα πράττῃ
καὶ λαλῇ, ἀλλ' ἵνα πολλάκις καὶ διὰ τὴν χρείαν τῆς
μετὰ σαρκὸς οἰκονομίας καὶ ὡς ἄνθρωπος λέγῃ τινά.
Athanasius contra Arianos 26, 221,28
ὁ δὲ τοῦ Θεοῦ Λόγος οὐχ, ὡς ἄν τις εἴποι, προφορικός ἐστιν, οὐδὲ ψόφος ῥημάτων, οὐδὲ τὸ προστάξαι Θεὸν, τοῦτό ἐστιν ὁ Υἱός· ἀλλ' ὡς φωτὸς ἀπαύγασμα, οὕτως ἐστὶ γέννημα τέλειον ἐκ τελείου.
Cyrillus frag. Pauli epistulam ad Romanos
ὁ γὰρ τοῦ Θεοῦ Λόγος ἐν εὐδοκίᾳ τοῦ Θεοῦ καὶ Πατρὸς ἐν ὁμοιώματι γέγονε σαρκὸς ἁμαρτίας