i have done something similar like noting exactly where each of my body parts are when i'm standing and after i get down on the shot,and one thing i notice is my vision center moves offline as i'm getting down (by a few mm's,not by much),so the cue ends up often very slightly more to the right of my chin instead of the correct place and it's enough to cause a miss.so now i always check if it's in the correct place when i'm down and my potting has improved but i still struggle sometimes to get the cue on the line consistently although it has improved.probably the solution is loads of practice on setting up with the exact same alignment over and over,no real shortcut.
Sounds like you are having some inconsistency in your setup with the cue relative to your body position rather than line of aim per se. What I mean is, the cue could be dead on the line of aim but since you have your head and eyes in a different spot than where you are used to sighting (when cue is directly under your chin), the skewed perspective makes it appear off.
While there is no 'shortcut' for setting up the same way over and over there are definitely techniques you could try to make that more likely and therefore minimize the amount of practice required to get it down. Kinda like Mullins said about shooting a basketball...If you have great technique you can get away with 200 shots a day, but with poor technique, you may need to shoot 1000. Same goes for getting into your setup.
Technique 1: Set up around the cue. This one has been mentioned above but I will add a few points. Once the cue is aligned on the line of the shot you take your stance around it by setting your feet, then coming straight down over the cue. The feeling should be of lowering straight down with no forward or twisting movements...you have preset those with your foot position. If you are tall enough for a dead hang of your arm to your cue, even your elbow should not move and feel only as if it is being drawn straight upwards (as a result of your body lowering into position)...assuming you are a hanging forearm stroke guy.
Technique 2: Preset your finish in your preshot routine and form a stance around that. This one is much less commonly used and mostly by those players who have their forearm forward of 90* to the floor at address and those who drop their elbows. The idea here is to complete a stroke in your preshot routine which will help you preset your finish position allowing you to get into your stance in a way that ensures you take out any twisting or slipping around of your grip between your address and finish positions (you will often see a slight bowed wrist in these players since that is where their shot wants to finish). This technique CAN WORK for other types of strokes as well and I would recommend you try it out no matter how you stroke the cue...
For your purpose, finishing a stroke while upright and seeing the alignment that your particular stroke wants to be in allows you to form your stance around this preset relationship of your body/arm angle.
So both techniques accomplish a high level of consistency; one by getting into position around a set cue which has been aligned to the shot and the other by getting your particular body-cue relationship preset before getting down on the shot line.
Hope one of these clicks for you.