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2 of 2 added that cleaning with dish soap seems to be possible, as suggested in comments

Use a "permanent" marker meant for writing on CDs on the containers directly. When storage is over, clean the writing with isopropyl alcohol.

The idea is similar to moscafj's, but unlike a nonpermanent marker, it won't smudge when you hold the boxes and move them around.

Update If you are uncomfortable using isopropyl alcohol, Pete Kirkham suggests in comments that dish soap plus elbow grease are sufficient to remove this kind of pen from a plastic box.