it seems to me as there is a bug with the shrinkwrap - boolean combo in Blender.
As you can see in the following image the red shrinkwrap geometry only touches
the cube in the center at with the end geometry of the half ring.
Without the boolean command the shrinkwrap modifier however perfectly projects
the red geometry onto the cube. The moment I add a boolean modifier to the cube
to cut the red object out the shrinkwrap result is kinda ignored and distorted.
Looks to me like a bug or is it a flaw in the way how the modifier data is passed down
to each object? Technically speaking the end of the modifier stack geometry the (the red
shrink wrapped ark) should be passed into the boolean modifier for the cube.
Here is a screenshot where the boolean modifier is turned off and the red object works perfectly.
Here is a video: