The difference in translation:
οἶμαι parenthetical:
Inasmuch as/because, I think, they are ambitious and aggressive and numerous, and they speak earnestly and persuasively, they have struck your ears, . . .
οἶμαι dependent on ἅτε might be:
Insofar as I think/in my view, being ambitious and aggressive and numerous, and speaking earnestly and persuasively, they have struck your ears . . .
I can’t say for sure that this is absolutely impossible, though it seems unusual.
But ἅτε with participle is a common idiom.
Smyth 2085
- With participles of cause (2064): ἅτε (ἅτε δη), οἷα or οἷον (οἷον δή) inasmuch as, state the cause as a fact on the authority of the speaker or writer. Thus, ὁ Κῦρος, ἅτε παῖς ὤν, . . . ἥδετο τῇ στολῇ Cyrus, inasmuch as he was a child, was pleased with the robe X. C. 1.3.3, ἥκομεν ἑσπέρα_ς ἀπὸ τοῦ στρατοπέδου, οἷον δὲ διὰ χρόνου ἀφι_γμένος ᾖ ἐπὶ τὰ_ς συνήθεις διατριβά_ς I returned in the evening from the camp, and, as I arrived after a long absence, I proceeded to my accustomed haunts P. Charm. 153a, ““οἷα δὴ ἀπιόντων πρὸς δεῖπνον . . . τῶν πελταστῶν, . . . ἐπελαύνουσι” inasmuch as the peltasts were going off to supper, they rode against them” X. H. 5.4.39. ὥστε has the same force in Hdt.
http://www.perseus.tufts.edu/hopper/text?doc=Smyth+grammar+2085&fromdoc=Perseus%3Atext%3A1999.04.0007
And οἶμαι is frequently parenthetical.
LSJ οἶμαι:
IV. [select] parenthetically, mostly in first person, ἐν πρώτοισιν, ὀΐω, κείσεται among the first, I ween, will he be lying, Il.8.536 ; “ἔπειτά γ᾽, ὀΐω, γνώσεαι” Od.16.309, cf. Il.13.153, Od.2.255, etc. : in Hom. only in act. form ὀΐω, exc. “ὀΐομαι” Od.22.140, and perh. 14.363, cf. A.Ch. 758 ; in Att. this parenthetic use is prob. confined to the shorter form οἶμαι, impf. ᾤμην ; rarely in other persons than the first, as οὐκ οἴει ἀναγκασθήσεται; Pl.R.486c, cf. Tht.147b ; πόσης οἴεσθε γέμει σωφροσύνης; Id.Smp.216d.
- [select] expressive of modesty or courtesy, to avoid over-great bluntness of assertion, Id.Grg.483c, X.Cyr.1.3.11, etc. : even between a Prep. and its case, “ἐξ οἶμαι τῆς ἀκροτάτης ἐλευθερίας” Pl.R.564a ; “ἐν οἶμαι πολλοῖς” D.20.3 ; or between Art. and Subst., “οἱ γὰρ οἶμαι βέλτιστοι” Id.54.38.
http://www.perseus.tufts.edu/hopper/morph?l=oi)%2Fomai&la=greek&can=oi)%2Fomai0&prior=oi)=mai&d=Perseus:text:1999.04.0057:entry=oi)=mai&i=1#lexicon