[Sachiel7]

Ohh..Goodie! Small team...
The good thing about a small team is that you can easily spread people over multiple groups. When a person comes up with a design idea, they usually are some of the best ones to build it (if they can) because they have the idea in their head. They also know how it integrates with the rest of the Robot. We usually Split up into 3 groups: Drive/Chassis Sub-Systems and Controls. Sub-Systems are any robot devices that work with game elements. The robot as a whole is discussed by the whole team, but each group is responsible for the construction and integration of their part of the robot.
But if you're on a 10 person (or so) team, I think you can do alot with the entire team. Design meetings can be held for anyone.
I like some of the methods Ken described, this is what we've been doing for a while, and it works pretty good. I think his and my method are pretty much the same thing, just explained differently.
But I agree, the FIRST thing that needs to be done is to identify the problem. In any engineering sense, that assists you in defining your goals. Once you have your goals, you come up with basic ideas to do them, like stacking - putting one box on another, then picking those up, etc. Then, come up with some basic drawings (sketches) of the shape of a device to perform that function. Elaborate on it more, and then define the proper actuation for the task.
But, I'm sure you've got that down. It seems you want more suggestions for the group dynamics involved in the design process.
I know what it's like being a team leader, It's not easy. These past years we've had about the same resources as that of what you mentioned, and we've developed some nice bots. When you're coming up with design, I wouldn't worry too much about the resources you have. Besides, other teams (like ours, maybe) are probably willing to open their work space for other teams to use. We did this in 2002.

Another idea is to ask the team how they want to handle the design process. You may be surprised that 90% of the team is thinking of the same process in their head. But Pre-Season would be a good time to get this laid out.
Just see what they think. If they don't have ideas, then give a few different options, and get feedback.