I've done S&F a lot more than OSH, but it seems to be the same at all the big shows.
See how much of your checklist and avionics setup can be completed in your parking space just by turning on the masters (flaps, trim, altimeter, frequencies, GPS waypoints, fuel selector, etc). Your goal is to get down to not much more than "canopy locked, all knobs forward, transponder off" when you arrive at the runway. You know, stuff you can truly do on the roll.
After start put your attention on your rolling taxi escort and nothing else. Runup can wait until you are released onto a main taxiway away from parked airplanes and pedestrians.
I don't think true rolling runups are a good idea. Somebody will run over the guy in front of them, only question being how often it will happen. Instead try to anticipate the stops and starts as the controllers position and release. When you're 5, 10, maybe even 15 from the front, kick it sideways like Gary said, stop, then get a quick mag check. At the next pause do it again and cycle the prop or check the carb heat if you feel the need.
Worried about holding up the line? Well, if you anticipate the usual stop and go you're unlikely to slow anything. Second, consider how inconvenient it will be for everyone if you prop chop the guy in front, or crash on takeoff, or otherwise cause an operations shutdown. Take the time to do it right.