Edit: "The Immunity Syndrome" with the backward facing engine room has the larger barrel facing away from the cathedral...
I think you are having the scene in mind where Kirk enters the engine room. But we do not know which
engine room that is.
If I'm not mistaken the decisive scene here was the point of view
from the (impulse and warp drive) EMM.
) the console and Scotty really block a good view of the dcca-housing, so it's hard or impossible to tell which "barrel" is next to the cathedral.