I use the same kind of setup, where the tasks keeps on populating my query of unfinished task. The only change related to your setup is that I’m using the - to denote canceled tasks.
So when I want to ignore/cancel a task, I hit the task text from the query, enter the - into the task field, and go back to the query, or continue onwards with other actions.
I’ve recently also posted a template to cancel tasks with a cancel date (for use on the task definition) which might be of interest:
I’m not using that, but you could add start dates to your task, and modify the query so it only includes tasks without start dates, or a start date in the past. That way you add push a task to next tuesday by setting the start date to that date.