Those grids were located in the northern hemisphere, whereas American Samoa
is in the southern hemisphere. This issue is acknowledged in the NADCON5 manual
https://www.ngs.noaa.gov/PUBS_LIB/NOAA_TR_NOS_NGS_63.pdf#page=36
"""The grids in American Samoa are in the Southern hemisphere, and this caused
them to be inadvertently stored in mirror image (south is north, north is south)."
So :
fix the registration of the grid to switch the sign of latitude
mirror vertically
and also negate the sign of the latitude correction
The result is consistent with what is obtained with the AS62->WGS84 Helmert
transformation and the https://www.ngs.noaa.gov/NCAT/ online service
For example given lat=-14.3178643343 lon=-170.8335399628 in AS62
Those grids were located in the northern hemisphere, whereas American Samoa is in the southern hemisphere. This issue is acknowledged in the NADCON5 manual https://www.ngs.noaa.gov/PUBS_LIB/NOAA_TR_NOS_NGS_63.pdf#page=36 """The grids in American Samoa are in the Southern hemisphere, and this caused them to be inadvertently stored in mirror image (south is north, north is south)."
So :
The result is consistent with what is obtained with the AS62->WGS84 Helmert transformation and the https://www.ngs.noaa.gov/NCAT/ online service
For example given lat=-14.3178643343 lon=-170.8335399628 in AS62
https://www.ngs.noaa.gov/NCAT/ : AS62->NAD83(1993) outputs lat -14.3129107343 lon=-170.8347552800
with the corrected grid: $ echo "-14.3178643343 -170.8335399628 0" | cct -d 8 \ +proj=pipeline +step +proj=axisswap +order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad \ +step +proj=hgridshift +grids=$HOME/proj/proj-datumgrid/north-america/wshpgn.gsb \ +step +proj=unitconvert +xy_in=rad +xy_out=deg +step +proj=axisswap +order=2,1 -14.31290935 -170.83475638 0.00000000 inf
with the AS62->WGS84 Helmert transformation: $ echo "-14.3178643343 -170.8335399628 0" | cct -d 8 \ +proj=pipeline +step +proj=axisswap +order=2,1 +step +proj=unitconvert +xy_in=deg +xy_out=rad \ +step +proj=push +v_3 +step +proj=cart +ellps=clrk66 \ +step +proj=helmert +x=-115 +y=118 +z=426 \ +step +inv +proj=cart +ellps=WGS84 +step +proj=pop +v_3 \ +step +proj=unitconvert +xy_in=rad +xy_out=deg +step +proj=axisswap +order=2,1 -14.31289451 -170.83478954 0.00000000 inf