Ok so first of all, just to be very clear, you never owed the IRS $764. You owed them $611, and you owed your state tax collecting agency $153. This is important because the IRS and state tax collectors are different entities and don't talk to each other. Sending the IRS $764 would not result in your state getting the correct amount of money, it would have meant you'd overpaid the IRS and your state collectors would be after you for the $153. This may be part of what's confusing anyone you might talk to at the IRS.
Money would not have been taken out of your account without your authorization. When you did your taxes, you probably input your bank information and ticked some box that directed each tax collecting agency to withdraw the money. Then you did it again via the IRS website. (As far as I know you have to input your SSN on the IRS site to make a payment, so there should at least be a clear trail on their end of what happened.)
Then you had your bank reverse the charge (for future reference, this should be a last resort) while the IRS had apparently figured out on their end that you'd overpaid and so issued a refund check (the physical check is probably because you hadn't given them authorization on your tax return to send electronic funds, since you were paying rather than getting a refund). This is why they came after you for $764: you overpaid by that amount, they were in the process of giving it back to you, then you pulled it back via your bank. From their perspective they had now double-paid you back.
Ok, you got the check from the IRS and handed it over to them, and were told it would take 60 days to clear up. It has not been 60 days yet. In the meantime their system still thinks they double-paid you back, and is dinging you for it. They are not trying to screw you. This is just bog-standard bureaucracy.
It's fine to be concerned about continuing to get notices, and you should maybe contact the IRS just to get reassurance that yes, once the thing with the check is cleared up the notices will stop coming. But what's actually happening here isn't the IRS fucking with you, it's that you made several mistakes, and the bureaucracy is slow in clearing them up.