Of course part of the lesson on Friday may be dedicated to finalizing or adding extra flourishes to a project. That shouldn't ever exceed 30 minutes. There is still the actual presentation part to conduct. (Are you working in your marking while they are presenting? Is there space for peer critique/questioning?) Friday is already so busy that there should be very little time to dedicate to still completing the work. What is not completed in class is homework. Plain and simple. Assign groups at the start of the week, make sure they know how to communicate with each other and every week, tell students that if they do not come on Friday, the will be marked as such and receive 0. Use your judgement for individual cases but the rule should be stated explicitly.
There are so many different ways that the test can be used on Friday: group work to figure out the questions that proved the most difficult for the majority of students; peer help - giving stronger students an opportunity to show off; making a game of the test questions to see what they remember from it; getting students to act out the complicated questions so that there is visual representation of what they are trying to grasp, and then working out the situation. These are just a few tasks that can be carried out.
Another biggie is feedback time. All that time spent on doing projects up to the last minute of class takes away their face to face with the teacher time. This is an important motivator and should not be swept aside. A few moments in private with each student needs to be worked in on Fridays.
Reflection is something we worked on during our last PD Day. There were lots of great ideas presented (video log, comic books, ...). Maybe we should workshop this again at the next one in April to keep things fresh and upgrade those ideas?
Keep the other great things you have worked into your Fridays. Some of you play music or get students to bring in treats for everyone to share. This is great! Friday has to be fun, a release, a triumph. We want them to know we are proud of them. We want them to be proud of themselves.