Eugenia Good idea and it is almost a well thought HR exercise. You may need to think of ways in which the group work is fun rather than a well thought curriculum. Also, you need to figure out how different microgroups will interact with each other and how if possible have all groups meet in clusters or a grand ball.
You have hit it bang on...at the core of what causes gratitude? There has to be a genuine reason for someone to show gratitude. What you are approaching from a problem solving angle, I am exploring it from the fact...that why and how problems of a company may come out. And I have created a Helpline...where people can share their 'problems' to be solved. Do read it...its called Thank God Its Friday - Office Helpline. I may have more ideas to build on your idea after I read your notes...and lots of synergies between our ideas.