Hm...And don't they need a gate key just to activate the portal? Is it necessary to have it to travel through the gate? If the answer is "no" then only one person, who holds the gate key, can send others through the gate and, after that, travel through time by him-/herself.
All we know about the max number of people who can go through at once. But the game itself shows (when Lucca arrives in 600 A.D. on her own) that individual time traveling is quite possible.
So the question is: for what exact purpose do they need a gate key?