Mark reviewed views
 

Is it possible under the Review perspective to only have projects that are due to be reviewed appear? Currently mine just moves them down to the bottom of the list after you hit "mark reviewed".

I want to hide all projects that have been marked as reviewed until their next review date

In the Review perspective, close the groups for future review dates, and save a snapshot of the perspective, making sure the Restore: Expansion box is checked. You'll still have the sections present, but you won't see the projects unless you open the future groups.