I am not sure if I am understanding your complete question, but here is what I do.
I set the Timing of my quiz to open on a Saturday and close on the following Friday. It is a 2 hour timed exam. Students can then take their exams anytime between these two days (7 days). I do tell them that the 2-hours is continuous, that they can't take 1-hour on one day and then another hour on another day.
In your description, it appears that you might want students to take the exam at a specific time, such as 8PM. If this is so, I ask you "Why?" Why is the time so important to you? I prefer to let students pick their time, and I even encourage them to pick a time when their brain works best. Some students are more alert in the morning, some in the evening. My method also supports students who might be in dramatically different timezones.