This verse is unusual after all: the fronting of that ἀξίως, the weird word choice of πολιτεύομαι. It's like the author wanted to pop it out, to trip the reader right here. A subjectless infinitive fits right in.
Secondly, what are you trying to say? The fronting of ἀξίως is interesting, giving the adverb the emphasis, but I'm not sure what you are trying to claim about πολιτεύεσθε. There's nothing weird at all about it. It fits the context and expresses Paul's thought just as he wished to express it. It's a rare word in the NT corpus, but not rare in general (and cf. Acts 23:1). And are you claiming the infinitive would somehow work better?
N.E. Barry Hofstetter, M.A., Th.M.
Ph.D. Student U of FL
Instructor of Latin
Jack M. Barrack Hebrew Academy
καὶ σὺ τὸ σὸν ποιήσεις κἀγὼ τὸ ἐμόν. ἆρον τὸ σὸν καὶ ὕπαγε.