Two notification problems when enabling "Online submission" for assignments that can *also* be submitted on paper

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I allow students to turn in all assignments digitally, which requires me to enable "Online submission" for my assignments. However, many of them prefer to turn them in a hard copy (which is fine by me).

Problem 1: If a student opts to hand in the hard copy and I enter the grade into the grade book for that assignment, the student's Canvas app continues to pester them to submit the assignment (even though I've already graded it!).

Problem 2: To stop the Canvas app from pestering them, students (reasonably) upload blank files. However, this means that Canvas now pesters me to grade a bunch of blank submissions (that I have already graded!).

Is there a way to allow online or paper submissions for one assignment? 

How else can we avoid these gratuitous notification problems?