I think it would be better to try taking google's 20% philosophy and making it a "Hey, do you have an idea? No? Well, join this team for the hackathon!" Run it

I think it would be better to try taking google's 20% philosophy and making it a "Hey, do you have an idea? No? Well, join this team for the hackathon!" Run it on four days a month in a row but during normal hours. This allows people to talk about it and not burn out. I'm assuming that most teams do not program in their spare time for fun. /IANAM