Imho, I wouldn't remove wood from 'the strong side' unless I felt SURE that it was indeed the problem. If thickness side to side is dead nuts accurate and the string grooves/nocks on the tips are properly crafted, it may be a simple alignment issue, so check that before you remove any wood. It takes seconds.
Similar to George, I use a single strand of bow string, weighted with heavy lead sinkers, and just drape it over the center of the tips, unstrung, then take note of how it bisects the handle. If all things are constructed well as noted above, I look to natural alignment issues like twist due to propellor, misalignment while unstrung due to warpage or movement after layout, etc. and then it's best to use heat to align things rather than removing wood from 'the strong side'.