The "reopen" a current attempt option in moderate restarts students with the time they have remaining at the time when I click the button. However, with remote teaching, coordinating that the quiz needs to be reopened, and the time that it should be reopened is very hit-and-miss. A student tells me a message that justifies reopening the quiz, and when I see it an hour later, the student is no longer online. I send a message requesting confirmation that the student is online, and they respond after I've gone to bed. It just goes on and on.
I propose a checkbox under the reopen button, to schedule (when checked) the time to restart when the student next accesses the quiz.