From the (simplified) project description and the following discussion, I more and more wonder why you want to go wireless, rather than wired, like just about all these fencing scoring devices do.
The timing of wireless signals is indeed a headache. Most if not all wireless protocols are simply not designed to be real time.
To do real time over wireless you'll have to deeply understand the complete protocol, from the lowest level up to the highest, plus the workings of the hardware. Then you can know the inherent transmission delays, chances of channel interference, packet loss and delay of retransmission, etc. Fencing is after all a game where milliseconds count, so any disturbance in the transmission may mean the difference between win and lose (and the cause of many an argument)