Maybe I'm missing something, but "Largest Overlap" doesn't make sense. Sometimes, joining features get joined to multiple target features, or multiple joining features get joined to a single target feature.
If it's based on the LARGEST overlap, shouldn't a feature only get joined once... to the target feature it has the largest overlap with? "Largest" means the most, not just a lot of overlap.
I'm having a similar problem. The target polygons are getting joined with the smallest overlapping join polygons instead of the largest! Did you ever get a solution?
Trying to revive this topic...
I have experienced the same issue as @Libra66 when my data is in a geographic coordinate system. Once I projected it to a projected coordinate system, it identified the correct largest overlap. Is there a bug here? Maybe the tool needs to be adjusted for geodesic area?