Since you specified the transformation you used, I looked it up in some reference material Esri provides on selecting a transformation to use - specifically, this pdf which lists available transformations in ArcGIS. It includes an accuracy column. Although there isn't any specific explanation of the numeric value, and mkennedy has noted it is derived from a third party source via unknown calculation, I make the assumption that lower is better (and theorize it means a point after transformation will be within x meters of original location, x being the accuracy).
You likely chose the transformation you did based on the name and that it was designed for that area, but the chart indicates a relatively inaccurate rating of 44 compared to some of the others that are near or below 1. So while that is the best transformation offered by default, matching that name, another one might give better results - including a custom transformation.
mkennedy found an article by a Prof. Mugnier giving parameters for another transformation for that area: ΔX = –83.7 m, ΔY = –81.9 m, and ΔZ = –131.6 m. Those parameters can be put into the Create Custom Geographic Transformation tool in ArcGIS to generate a custom transformation file that can be applied instead of picking one of the defaults/included. These parameters may (and apparently they or another set have) provide a more accurate result.
The actual details of why that particular transformation has the accuracy it does gets into math and geodesy that's over my head.