Thanks guys.
Comments on the chicken forums about the bucket traps indicate that some people use them as live traps by leaving the water out. Moot point - it’s caught nothing, and there are no signs any rat has fallen in and escaped.
The chicken coop can’t be moved. It’s not really high off the ground - it sits on sleepers. It’s about 3m x 2m x 3m, and while in theory with assistance it might be possible to move it, fences have been constructed around it.
We set the snap traps, and the first night we got three rats. Two were clean kills, but the cheapest of the three traps I bought snapped on the rat’s face without killing it, just injuring it. While we were trying to get the trap to put the rat out of its misery, it escaped. Poor thing. We feel awful. We’ve disabled that trap and we’re getting rid of it. The other two traps have failed to catch any rats over the three nights since.