Clear text passwords in and of themselves are not a problem. The problem is with the risks associated with that data. What is the impact to the users, and what is the impact to the company if this data is leaked, disclosed, lost, or corrupted? What if it was publicised that this data was in the clear, as you describe?
If there are no risks, then it does not make sense to implement costly controls around it.
If there are risks, then the controls need to be scaled with those risks.
I know that it is easy to say, "OMG! Clear text passwords from a web app in 2016?! What kind of a company is this? There are numerous libraries that the devs could have called to take care of this from the beginning!" I know I did when I read your post.
But at this point, changes to the environment need to make sense in terms of the risks involved. Your job is not to come up with the most compelling technical or security argument (if one of those arguments would have worked, then the problem would not exist). Instead, your job is to quantify the risks to the company and propose a control appropriate to those risks to mitigate them. That's how you proceed.
If the risks are high and costly and they are still not interested, then ask them if their fire insurance is paid up. Small investments can stave off massive losses, just like insurance.
If you still cannot get them to deal with this, then you are left with the unfortunate, yet valid, situation of leaving this business decision in the hands of the business. They bear the risks. You gave them the needed info to manage those risks appropriately. There is not much else you can do.
But before you get to the fatalistic stage, get a good discussion going around the risks and how you can help them limit the company's exposure.