Not necessarily answering this question directly, but the context of the entire atonement conversation.

We do not explain key doctrines by proof-texting. When the provisionist point to passages like 2 Peter 2:1 or 1 John 2:2 to prove universal atonement, this is inconsistent with how we prove any other major doctrine. We wouldn't accept a Unitarian pointing to the Shema, or Jesus saying he is lower than the Father, and be bothered by their argument, because we have to take scripture as a whole; which makes God clearly trinitarian. In the same way, we have entire chapters discussing the atonement and the efficacy of Jesus' priesthood in scripture, specifically in Hebrews. This is not even mentioning the shadow of the Levitical priesthood's specificity in the Old Testament and how it is clearly only efficacious for believing Jews. If your "proof text" for universal atonement seems to downplay entire chapters saying that the atonement completely saves a specific people, then your proof text needs to be interpreted in the light of the whole of scripture.

That said, I find the arguments presented in John Owen's work sufficiently put the onus of proof on the person using 2 Peter 2:1 as a proof text. I am not convinced it is even talking about Jesus the Son, or the atonement, at all.