[EricH]

Is it possible to test on carpet before the demo? This can tell you if you do indeed have a problem. Just be sure to use a length of wire to touch both the robot and ground first, before any humans come in range. (If you hear anything when you do, you know you have an issue.)

As for a wood stage and dragging a wire, unless there is a channel for electricity off of the wood, there will most likely not be a benefit, due to wood being a lousy conductor in general.

Do you have any tread lying around? That isn't too hard to screw into the wheels with wood screws or other fasteners, especially if you aren't planning to play in an official competition match again. This is the same as using duct tape, only a little bit more sticky towards carpet. (Trust me, those treads can stick to carpet. They can also leave tread marks, so maybe this isn't the best idea.) Fabric may also work.

Or, here's an "easy" one: Bring regolith with you, if you have any, and run on that if you have a decent amount. It's almost light enough to carry, especially in smaller chunks. (For reference, one of the rolls used in official FRC matches this year was about a 4-5 person carry.)