My concern is how to determine what is a good dose of ketamin to tranq shot a T-rex? We don't know for sure the first T-rex on sight will be an adult or a juvenile but with such tight deadline there is no time to be picky.
Your hunters know how long it takes for ketamine to effect a crocodile. Let's say it takes 5 minutes. They suspect a T-rex has a faster metabolism than a crocodile -- they are closer to warm blooded birds than cold blooded crocodiles after all -- and so the correct dose should take hold in less than 5 minutes.
The first T-rex you see, check is he bigger than a crocodile. If not let him go, he's too small to be any fun. If he is big enough he gets a crocodile-sized dart. Follow him for 5 minutes.
If the T-rex is asleep scoop him up. Otherwise shoot another dart to double the dose.
Follow for another 5 minutes. Is he asleep yet? If not then shoot two more darts (or one dart with double the dose). Now he has 4 servings of Ketamine in his system.
Keep doubling the dose and waiting. Eventually when he falls asleep he has no more than twice the minimum dose.
Edit: L. Dutch's answer suggests the lethal dose for crocodiles is only about twice the minimum sedative. That's bad news for our hunters, since the above method might accidentally kill the t-rex.
To fix the method replace "double" with "multiply by 1.1". That way you need more darts but when the T-rex falls asleep you have used no more than 1.1 times the minimum sedative. The doses look like this:
The blue graph is the total amount of ketamine after $n$ shots. The red graph is the amount to put in shot number $n$.