How to pass a custom product attribute to the mini-cart?

You should not “override” a standard class in Magento 2, because you will break all the other poor-written extensions, which try to “override” the same class too.
Learn and use the plugins.
See how is a mini-cart rendered.
As you can see, the \Magento\Checkout\CustomerData\DefaultItem::doGetItemData() is called only from the public \Magento\Checkout\CustomerData\AbstractItem::getItemData() method, and you can use an after-plugin for it and modify its result.