This is a custom plug-in called ‘Way of Music’, would it be possible for you to show us where in the code of your plug-in we can simply add the product type ‘Rental Product’?
We’ve had the same issue with the ‘BEAR Bulk Editing’ plug-in, where we couldn’t edit our ‘Rental Products’, and their support showed us in the code where we can add additional products to make it work.