Answer
For the Database Task case specifically, a working technique is to export an existing Database Task as XML, edit that XML to reference your own package and procedure (YOUR_PACKAGE_API.YOUR_PROCEDURE) along with its correct parameters, and import the modified XML back in — this creates a new Database Task calling your procedure even though it was never selectable through the normal New Database Task method LOV, and the same approach works for making otherwise-unlisted core methods available as Database Tasks too.