You can create a button on cards to make a copy into a specific list without due date.
Not sure how much time that saves you ultimately, since you have to open card to hit the button, and also send it elsewhere if you want it in another list or board.
![Screenshot 2023-09-13 091902.jpg Screenshot 2023-09-13 091902.jpg](https://community.atlassian.com/t5/image/serverpage/image-id/280468iC07167C9F420C20E/image-size/large?v=v2&px=999)
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