Proper investigators would catch the killer after the second death

I suppose we can assume they didn't think of it. I didn't notice that Lucas walked into the room and didn't drink any coffee until my second watch. And they wake up with only twenty minutes to go until the next trap. So they have to solve a time-sensitive problem, and searching every person's blood would take considerably longer than twenty minutes. And I think at that point they were all convinced Gabe was the killer. It wasn't until the next trap went off that they started suspecting each other.

I feel like if any of them had done any sort of investigation of even the first crime scene they'd have figured shit out a lot sooner. These people are all supposed to be agents/detectives yet they all seemed to go into Average Citizen mode after the first murder.

But you're right, that's the first thing Kilmer points out in the forensics lab, that they can do blood tests.
True, by the time they woke up they didn't have enough time before the next trap to run all of their blood tests, but they could've at least started the tests. But nope, they just dumbed their way to death.