“As Achan’s family was held responsible for his sin (Joshua 7:16-26), so it is with Adam’s family.”

Poor example for 2 reasons:

1. The law of God explicitly states that guilt doesn’t transfer from parent to child: “Fathers shall not be put to death for their children, nor shall children be put to death for their fathers; a person shall be put to death for his own sin.” (Deuteronomy 24:16)

Ezekiel 18:20-25 again establish that sons do not bear their father’s guilt, and that this is in fact ‘God’s way,’ with the notion that children should bear the guilt of their parents being shown to be a fallen, human invention. Assuming that the Israelites were doing right in executing Achan’s family, an easily justified inference is that those in Achan’s household were willful accomplices to his sin.

2. While there can be broader collective punishments upon a people group, this doesn’t necessarily imply personal guilt (e.g. 1 Kings 14:13).

…he present tense would have been a much better choice for Paul in this context.

It’s quite normal to speak of already existent processes in aorist terms, even if the process begins (or is beginning again) with more individuals, compare:

“For by one Spirit we were all baptized into one body…and have all been made to drink into one Spirit.” (1 Cor 12:13)

“In Him we have obtained an inheritance…” (Eph 1:11a)

“All people die because of the one sin of Adam.”

I agree to an extent, but physical death is not indicative of personal guilt, otherwise Christ could not have died.

“…then we must state that we have Christ’s righteousness imputed to us only when we act as Christ acted.”

Not quite: We have Adam’s sin imputed to us when we identify with him (by sinning as he did), and have Christ’s righteousness imputed to us when we identify with Him (through faith in Him).

“Christ’s righteousness is imputed to us without any participation of our own, just as Adam’s sin is imputed to us without our consent.”

Righteousness is by faith, and believing is definitely a participatory act. By that, if our identification with Christ is through a form of active participation, then our identification with Adam would be through the same.

Additionally, the voice for ’sinned’ in Romans 3:23 and 5:12 is active, rather than passive or middle. An active verb refers to what the subject does, not something done to it. Therefore said references to sinning in Romans necessarily refer what the individual actually commits, not something mysteriously thrust upon him. Paul frames the guilt of the sin that killed him spiritually not as some inherited baggage, but a result of his own nature coupled with a realization of the law of God.

“Once I was alive apart from law; but when the commandment came, sin sprang to life and I died.” (Romans 7:9)

Michael Horton, in his book, Christless Christianity: The Alternative Gospel of the American Church makes the assertion that Pelagianism is the “default setting” of the human heart.  I can practically see your eyes glossing over right now…….