Shoot any others nearby so you can work undisturbed and retrieve the dynamite. Save game here. Go to outhouse and open door. Ignite and toss dynamite just in front of seat. Anywhere else Might succeed but in front is the sweet spot.
Panel blows off exposing the green waste stream.
You are in a room with a large gray disk. Circle disk to the door and open it. 2 grays are seen with a cow suspended on a pole between them. Another gray's face appears and the door is closed. Return via waste stream to outhouse and climb out.