If I use "EBGaramond-Initials.otf" instead of "EBGaramondInitials.pfb"
in the map file for dvipdfmx, I obtain decorative initials also in the
case of dvipdfmx:
Good that there's a workaround, but that still indicates a bug in
dvipdfmx's type1 handling. (Or, less likely, in the original font
generation, I suppose.)
k