How are you planning to run it with a 3 group? Have one barista on each end of the machine or are you planning to run 2 stations? At a minimum you would need 2 machines to make any kind of feasible competition.
From what I see, 15 minutes is an extraordinary amount of time for a minimum of 2 coffees to be served considering they also have 15 minutes prep time and coffee may be pre-ground (although this will obviously score low in the tech sheet for understanding the grinder).
I think a re-write in the rules is in order. Perhaps you could stipulate how many coffees need to be served rather than leaving it up to the barista how many he would like to serve. Once you have that, you can set a stricter time frame. Say 10 minutes prep time, 10 minutes presentation time, 10 minutes clean up. More than enough time to make 2 drinks.
This way with 2 stations and running an extremely tight ship, you can knock out all of the 12 run throughs in 120 minutes. Everyone knows that never really happens, so say 150 minutes or 2.5 hours.
My 2 cents as a competing barista.
All the best.
PS: re machines, why not hit up a local coffee roastery for a machine. They must have a machine they can let you borrow for the day if you give them a plug during the comp (unless you have a coffee sponsor in which case you could ask them for machines!)