Having a discussion with upper management about morale equaling productivity isn't going to work in your situation. You will need to show them. They will need to see the numbers and how it can work. Unfortunately not all people are visionaries but need to actually see before they believe. They have no faith.
I would consider being a little more proactive with my team. I would think outside the box meaning of course there are certain set rules in place but where there are no rules you would have liberty. Unfortunately for you, some of your most brilliant ideas have already been shot down before testing them.
The next great idea you come up with before you shop it around to upper management, develop a written plan, set a time line, measure the true productivity coming from your team. After the determined time frame has passed you will present the analysis of the output of work to your upper management with tangibles and it could become a new way of doing things.
Many people here have suggested food as an incentive and it does and can help your team become more productive and cohesive. We used to celebrate birthday's of the month when I first started working at my job. For one entire year, we had some kind of food with cake and soda's to celebrate whomever was having a birthday. We always had this kind of party the last Friday of the month. After a year the person implementing this great idea found a new job and moved on. No one took up the mantle of party throwing. Everyone participating would contribute $5.00. It was simply great. I think the hardest thing was getting the cake to the job.
Impromptu breakfast is always nice and relatively inexpensive. Mini bagels, orange juice, coffee, tea, fresh fruit, mini muffins and what ever else you can think of is also very nice.
But I think showing the output after implementing a plan would be better than going to a negative management to try to get things turned around. The numbers never lie.