I guess we're getting into differences of opinion at this point. The way I understand God hardening the heart vs giving them over to reprobate mind would be that for the former, God would be the cause of their rejection. For the latter, they were the cause of their rejection of God and God allowed them to have what they desired.
I can provide a human example. When our daughters were young I often found myself instructing them to dress warmer for the bus ride to school in the morning during the winter. My reasoning was that they would be prepared if the bus would break down or something. But, as with pretty much all children these days, they just didn't want to wear boots and hats and mittens to school. That would be uncool. Eventually, as they got older I began to back off because I figured they heard it enough and were getting old enough to take some responsibility. One time when they were riding with me and we had a snow storm so the country road leading to our home was covered with snow drifts we got stuck and had to walk home (about 1/2 mile). All they had on their feet were tennis shoes. A half mile doesn't seem too far but when you're walking in knee deep snow your feet will get plenty cold. Needless to say, they learned a lesson.
I didn't cause them to disregard my instructions by somehow hardening their hearts. The chose that for themselves. I did give them over to their own desires and as I hoped they got a strong lesson out of it.
I hope that helps show the difference.