Hey Thad,
I tried the JP2 you linked to and had no problems displaying the raster layer in my ArcGIS Runtime app.
So I inspected both JP2 files in Notepad++ and my JP2 file does not have the ProjectedCRS tag.
However my FeatureCollection does contain some informatorn about the spatial reference.
Here's where the info about spatial reference is stored in my JP2
<gml:origin>
<gml:Point srsName="urn:ogc:def:crs:EPSG::32755">
<gml:pos>309749.000000000000000 5818934.000000000000000</gml:pos>
</gml:Point>
</gml:origin>
<gml:offsetVector srsName="urn:ogc:def:crs:EPSG::32755">0.500000000000000 0</gml:offsetVector>
<gml:offsetVector srsName="urn:ogc:def:crs:EPSG::32755">0 -0.500000000000000</gml:offsetVector>