That stands to reason, and good thinking.
I tried it, it worked great. I also made something similar with the 4th and 6th axis.
For the 4th, I put robot it that position:
I mesured from a fixed part of the tool to a centered machined part at the base of the robot. Rotated J4 by 180° until both mesure were the same.
For the 6th I put the robot in that position:
Then again I mesured from a fixed part of the tool to a centered machined part between the 3rd and 4th axis. Rotated J6 by 180° until both mesure were the same.
One robot went from +/- 8mm to +/-4mm and the other from +/-5mm to +/-2mm
The difference is barely visible when looking at the mark. I'm currently working on a similar process for the 3 first joint, but I'm not sure I will find something.