I am not particularly clear about your goal. But I'd like to say a few things.
First, using GPS/DGPS to measure which team reaches the finish line is inaccurate. Raw GPS data is horrible in accuracy (varying in 1 - 10 meters, well, around that), also the sampling rate of a GPS module is low (say once a second?) How do you determine exactly which team reaches the finish line first?
Second, to use a mobile ZigBee chip to communicate in real-time is hard. I assume your stick has a ZigBee end device. When it is moving (which in your case is pretty fast), it must dynamically find and associate with new parent routers, which takes time and depending on the wireless environment, it might involve several retries. So you will imagine a packet is only successfully delivered to the other end after 100ms or even a second. This might not be a problem if your stick records the exact time when a team reaches the finish line. Since you have a GPS module in the stick so there is no problem in getting very accurate time.