Okay, I have an update - in case someone is interested and I manage to solve this, it is possible to see my steps for the progress:
I used a custom module with a plugin to override the magento model which initiates the pdf:
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
<plugin name="overwrite_m2e_amazon_order_pdfinvoice" type="MyVendor\MyModule\Plugin\Model\Order\PdfInvoice" />
This is working great. I tested this by creating a class which is calling the invoice pdf in exact the same way, M2e is doing this in vendor/m2epro/magento2-extension/Model/Cron/Task/Amazon/Order/SendInvoice.php on line 245 - 253.
With my plugin, the desired PDF is created. Without the plugin, the old magento default PDF is created.
If I know upload this and check what M2e is doing in the situation of creating a new invoice, I see the following error message:
And this is very confusing.
I did not found any ocurrency of this metadata anywhere in the m2e code. Furthemore, I did not change anything other than replacing the method for rendering the pdf.