The two readings derive the noun from different senses of the same verb stem, and the biblical text supports each in different passages. The offering is required where no wrong has been done, which favours the purification reading, but the same chapters use the ordinary language of forgiveness, which does not.
What would resolve this This is a question of interpretation rather than of missing evidence, and it will not be closed by a discovery. What would advance it is a full account of the class that explains the childbirth and discharge cases and the forgiveness formulae together, rather than treating either group as residual.
OpenHebrew Bible philology, Priestly source criticismJacob Milgrom, Leviticus 1-16: A New Translation with Introduction and Commentary