Looking for the fastest way shoot video on a camera and review it on a laptop
look for a camera that can trigger recording on/off by it's HDMI output (used when you have something like a atomos recorder), not sure which current models can/can't but any dslr that's marketed as a video camera should do it. 
run a hdmi cable to a hdmi capture box ( I think HDMI can do 15m without a repeater ) 
hook the capture box to a laptop 
use software that will start recording when the camera presses record. 
use software like stream to me 
coaches can use another device ( tablet/laptop etc ) to display the recorded run


Using this setup you can have the camera recording runs while multiple people can stream any previously recorded run at the same time. As long as the software can detect the record flag from the camera the whole process is automatic, playback can begin for a file the moment after recording has stopped. 

I'd recommend a black magic thunderbolt ultra studio mini
for the capture box, it comes with Media Express software which will auto trigger when it receives a record flag from the camera. The mini is bus powered &amp; small so it's keeping your cables down &amp; means everything is running of batteries if needed

Stream to me is an iOS app for the playback but the companion app Serve to me is Windows &amp; Mac &amp; that lives on the laptop watching the folder that Media Express records too. Alternatively I'm sure a bit of google will find an android substitute for this part of the link. 

All that reasonable cheap, meets the need of recording while simultaneously playback (actually a pretty hard thing to do without spending big bucks) &amp; once it's setup should take care of itself, while you concentrate on practice.