Oh hey Ian - Sorry, I didn't notice it was you. Cool idea for Build18. Here's a couple of ideas off the top of my head:
Even though you said you want something more than an Arduino, I'll point out the RobotOpen stuff:
http://www.andymark.com/product-p/am-2316.htm which has driver station software that comes with it. I used the
Sasquatch board (now out of production) on an FRC-scale robot last year and was happy with it. The RobotOpen stuff that's still available now unfortunately is somewhat awkward to build a control system with, since you need a digital sidecar to go along with it, and I'm not sure what the timeline is like for the release of the
next board. Running an IP stack on an Arduino is possible if you get one of the ethernet-enabled boards.
Since you're hacking together something that doesn't necessarily need to survive long-term, one option would be to program all your logic on a PC and use
USB interface boards to control the devices. If you're driving things open loop, this will probably work fine; getting a real-time control loop to work might be harder. Since you already have laptops, this is probably the most cost-effective, though you would have to write your own comm software if you want Wifi control - another option would be to use wireless joysticks, depending on the range you need.
Another option if you don't need Wifi would be to use a
Vex controller.
Other than that, any board that can drive servos can control FRC speed controllers. I know there are several products available that breakout servo headers for the RPi, for instance.