Could it be that the reason was that you posted images via a bot and so had no human element in your accounts any more?
What Instagram wants is good content or people will stay away. They know exactly who is botting, no proxy will ever prevent that - it's just too easy to collect that data, because no human acts like a bot, being online for hours and hours and following very large numbers of people.
So I conclude that it's not the botting (you had conservative settings), but the content that got you banned.
Try to post manually on the accounts you get back.