Thanks everyone. Keep the great ideas coming. It is reassuring to know I have already been doing some of these things without really thinking about why.
Back in February I organized our first every cooking competition campout. We had each patrol plan out a lunch, dinner, dessert, and breakfast. The adult leaders and SPL got to score each meal based on taste, presentation, creativity, etc. It was a close battle, but in the end, it was the oldest scout patrol that actually won the competition. They participated and really seemed to enjoy it.
At our last meeting, we have to two youngest patrols play a game involving tying bowlines and 'rescuing' their patrol-mates. The same older patrol facilitated the game and again had a good time and was not disruptive.
I definitely agree with Twocubdad that sometimes you have to dictate/mandate from the SM position if you want to change the culture. It is not necessarily that they boys don't want to do things, but more that they don't know how. When you show them, they will pick up with it.
One of the next things on my list is getting the boys planning meeting activities. We have discussions in advance and I ask them what do they want to do at the next meeting or two. Blank stares or sarcasm all the way around. I will suggest why don't we do x, y, and z and they will all agree. I am hoping that at some point they pick up on this and actually bring some ideas forward.
Thanks for everyone's help. I am learning a lot here. Keep 'em coming!