The parcels are, of course, horizontal only datum.
from the .prj

PROJCS["NAD_1983_StatePlane_New_Jersey_FIPS_2900_Feet",
GEOGCS["GCS_North_American_1983",
DATUM["D_North_American_1983",SPHEROID["GRS_1980",6378137.0,298.257222101]],
PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],
PROJECTION["Transverse_Mercator"],PARAMETER["False_Easting",492125.0],
PARAMETER["False_Northing",0.0],PARAMETER["Central_Meridian",-74.5],
PARAMETER["Scale_Factor",0.9999],
PARAMETER["Latitude_Of_Origin",38.83333333333334],UNIT["Foot_US",0.3048006096012192]]

and from a representative flood map .prj

PROJCS["WGS_1984_Web_Mercator_Auxiliary_Sphere",GEOGCS["GCS_WGS_1984",
DATUM["D_WGS_1984",SPHEROID["WGS_1984",6378137.0,298.257223563]],
PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],
PROJECTION["Mercator_Auxiliary_Sphere"],PARAMETER["False_Easting",0.0],
PARAMETER["False_Northing",0.0],PARAMETER["Central_Meridian",0.0],
PARAMETER["Standard_Parallel_1",0.0],PARAMETER["Auxiliary_Sphere_Type",0.0],UNIT["Meter",1.0]]

which seems now, looking at them, should just be a standard transform. But then 
this from
Adv_MO_FloodZones.shp.xml 

-<geodetic>
<horizdn>GCS WGS 1984</horizdn>
<ellips>World Geodetic System 1984</ellips>
<semiaxis>6378137.000000</semiaxis>
<denflat>298.257222</denflat>
</geodetic>
</horizsys>
<vertsys>
    <gridsysn>NAVD88</gridsysn>
    <plandu>FEET</plandu>
</vertsys>

well, I'll continue to muddle and head scratch.
----------------------------------------
> From: g...@ir.bbn.com
> To: sgl...@hotmail.com
> CC: gdal-dev@lists.osgeo.org
> Subject: Re: [gdal-dev] Fema Flood Maps NAV88 - proj4text
> Date: Sat, 2 Feb 2013 08:21:11 -0500
>
>
> You may want to join the proj list.
>
> Your parcel maps are in EPSG (ESRI, really) 102711, which is:
>
> http://spatialreference.org/ref/esri/102711/
>
> This is a horizontal-only datum. I have only encountered horizontal
> data in parcel maps (Mass, not NJ). Do you have any heights presented
> with this? If so, do you understand what they are? If there are
> heights, I would expect they are in NAVD88, but they could be in
> ellipsoidal height relative to the GRS80 ellipsoid and the NAD83
> orientation. Ellipsoidal height is relatively recent, and estimated
> orthometric heights based on geoid models and observed ellispoidal
> heights is where NGS is heading, but I would doubt most practitioners
> are doing that yet.
>
> Your flood maps are in EPSG:5703:
> http://spatialreference.org/ref/epsg/5703/
> This is a vertical-only datum. Are there horizontal coordinates? If
> so, what are they in? I would expect some sort of NAD83, and their
> purpose is to locate where the heights are given.
>
> So what I think you want is to know the NAVD88 heights around the parcel
> of interest, so you therefore want all your horizontal coordinates in
> NAD83, and to leave the height in NAVD88. (Water flows downhill in
> NAVD88, but does not necessarily flow towards lower height values in
> ellipsoidal height coordinates!!)
>
> You were talking about a geoid file, which presumably transforms NAVD88
> height to something, which is probably ellipsoidal height based on
> NAD83. That's the typical geoid model published by NGS.
> There are also geoid models from WGS84 ellipsoidal height, but these do
> not transform to NAVD88.
>
> Do you have any height data in other than NAVD88? If so, please
> describe it.
                                          
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