>> 3. AF at a particular distance, recompose, and then trip the shutter using the interval timer.
Are you using the "Self timer" activated from the shooting mode dial on the top left camera, or are you using the menu based intervalometer?
I don't know why it would matter, or if it would matter but if anyone is going to try to reproduce it they would want the identical settings.
What is your AF-C priority mode setting (custom a2)?
I am very sure I don't have the problem you are having but I may be skinning the cat differently. The key, as mentioned previously, is to have "AF Activation" (custom menu a5) set to OFF. And you seem to be sure you have that set correctly.
AF-S mode would not solve the problem because the camera would not fire. Same if in AF-C focus priority mode.