Here's how I see it:
Moses put on the veil which in turn created a blindness re: the temporary OC. That blindness of mind/thought re: the OC 2Cor3:14 is the veil on their heart 2Cor3:15. It's internalized misunderstanding.
I don't see it as judicial hardening as in Isaiah.
Although there is the look of simultaneity in Paul's verbs, word order looks to make the active voice turning first and the subjunctive shows potential which IMO shows human volition. The Gospel of Christ - the ministry of righteousness 2Cor3:9 - is assumed before the active turning. The ministry of righteousness concerns the exceeding glory of Christ over Moses and the end of the glory of Moses.
Jesus was dealing with this when here John5:46-47.
John 8:43 for example tho, judicial hardening? it certainly exists; His sovereignty overuling human agency.
we rebuff at this, thinking it unfair, but Paul specifically addresses any judgement of God we might make about this saying in Romans, who are you oh man to answer back to God?
why would that verse exist if our volition is the only thing in play?
imo too many of us simply decry reformed theology as evil, presuming any talk of God initiating our calling and election as being complete hyper-Calvinism, and do not stop to consider that there is much in scripture written about our will being subject to His.
we certainly are culpable for our decisions and actions, rightly so, and express a freedom of our will - - but that will is not completely free, nor are we ever independent of God able to do anything, for, the hearing ear and seeing eye and even the heart that is able to understand, He has made these things. we cannot boast