Roman 5.1-11 translation — Genitive Absolutes and Tenses

Here is my translation:

Therefore, having been justified by faith, we have peace with God through our Lord Jesus Christ, through whom we also have access by faith in this grace in which we stand, and we rejoice in the hope of the glory of God. And not only this, but we also rejoice in tribulations, knowing that tribulation produces patience, and patience produces character, and character produces hope. And this hope does no put us to shame, because the love of God has been poured out in our hearts through the holy Spirit, who was given to us. For while we were still weak, at the appointed time, Christ died for the ungodly. (For rarely will someone die on behalf of a righteous person, but perhaps for a good person someone would dare to die.) But God exhibits his love for us, that while we were still sinners, Christ died for us. Therefore, since we are now justified by His blood, much more will we be saved by Him from God’s wrath! For if we were reconciled to God while we were enemies through the death of His Son, much more, because we have been reconciled, will we be saved by His life! And not only this, but we also boast in God through our Lord, Jesus Christ, through whom we have now received reconciliation.
(Romans 5.1-11)

The italicized sentence is verse 6, which looks like this in the Greek:
ἔτι γὰρ Χριστὸς ὄντων ἡμῶν ἀσθενῶν ἔτι κατὰ καιρὸν ὑπὲρ ἀσεβῶν ἀπέθανεν
The bold words are a construction called a “genitive absolute.” A genitive absolute is when you have a participle [a verbal adjective] and a noun/pronoun in the genitive case that differs from the main subject and verb of the independent clause. In this example, the genitive absolute is “we were” while the subject of the independent clause is “Christ.”  They are loosely connected.  Another example of this is “while he was talking to her, I went to get a book.”   The subject of the independent clause is different than the subject of the independent clause.

When you come across a participle in Greek, the tense of the participle (in this case, present tense) tells us the kind of action the verbal aspect of the word is performing [i.e., progressive, undefined, perfected], as opposed to the time the action is performed [i.e., past, present, future].  The time of the action of a participle is determined by the tense of the main verb.  My question is whether this is still true of a genitive absolute?  Does it still carry the time of action of the main verb, though it is grammatically unlinked to it?

I realize that time of action is a touchy subject with verbs, especially aorists, which are undefined by definition.  The fact that “died” is past tense seems a given, since Paul is writing after the event.  With this in mind, I translated the genitive absolute also in a simple past tense, with the assumption that the time of the participle still piggy-backs off the main verb. Was I wrong to do this?