The verse appears as follows in the Greek New Testament.
1 Peter 4:6 (GNT)
6 εἰς τοῦτο γὰρ καὶ νεκροῖς εὐηγγελίσθη ἵνα κριθῶσι μὲν κατὰ ἀνθρώπους σαρκὶ ζῶσι δὲ κατὰ θεὸν πνεύματι.
[NOTE: Arland et al. (2012) note no variants of this verse extant.]
There are three verbs in this verse:
εὐαγγελίζω = Aorist Passive Indicative (3 person singular) = "the gospel was preached"
κρίνω = Aorist Passive Subjunctive (3 person plural) = "they may be deemed"
ζάω = Aorist Active Subjunctive (3 person plural) = "they may live life"
In respective to these verbs and tenses, the literal sense of the Douay-Rheims 1899 American Edition provides the best translation.
1 Peter 4:6 (Douay-Rheims 1899 American Edition)
6 For, for this cause was the gospel preached also to the dead: that they might be judged indeed according to men, in the flesh; but may live according to God, in the Spirit.
The indicative mood indicates certainty ("was the gospel preached"), and the subjunctive mood indicates possibility ("they might be judged") and ("may live"). So the modified sequence proposed by the Original Post would be as follows:
1) the gospel is preached >
2) they may be judged according to men >
3) they may live according to God
In simplified terms, the idea here is that all men are born dead in their spirit (Rom 5:12), and so to-the-dead is the Gospel preached (aorist passive indicative), notwithstanding that these dead may be deemed (aorist passive subjunctive) as still-living mortals from the viewpoint of man. The desired end state is that these spiritually dead may live (aorist active subjunctive) according to God in spirit, so as to become spiritually alive and thus become "the living."
Both verses bring these thoughts together:
1 Peter 4:5-6 (Douay-Rheims 1899 American Edition)
5 Who shall render account to him, who is ready to judge the living and the dead. 6 For, for this cause was the gospel preached also to the dead: that they might be judged indeed according to men, in the flesh; but may live according to God, in the Spirit.
To recap, "the dead" and "the living" in this context are categories of living people; the difference is that the former are dead in spirit, notwithstanding that anyone may deem (or judge) them as mortals still living; and the latter are no longer dead spiritually, because they are now alive to God in spirit.
Arland, Kurt et al. (2012). The Greek New Testament. Stuttgart: Deutsche Bibelgesellschaft, 794.