How do I transform a projection that is not part of a spatial_refice?

I am importing shapefiles into Postgres + PostGIS database.

Here's my usual routine:
* Find the srid in the spaces_ref_sys table where the srtext appears in shapefile.prj

* Load the data into a new table using the shp2pgsql utility specifying the srid with the -s flag
* Add the new table to my main geometry table and in the path convert to srid from 4269 (standard census projection) using ST_Transform

Unfortunately, the spaces_ref_sys table does not include the standard projection of Mississippi. The content of their .prj file looks like this, where I have highlighted the parts that I usually try to match:

PROJCS ["mstm", GEOGCS ["GCS_North_American_1983", ZERO ["D_North_American_1983", spheroid ["GRS_1980", 6378137.0,298.257222101]], PRIMEM ["Greenwich", 0.0251, block 0.0433 ]], DESIGN ["Transverse_Mercator"], PARAMETER ["False_Easting", 500000,0], parameter ["False_Northing", 1300000,0], parameter ["Central_Meridian", - 89.75], parameter ["Scale_Factor", 0.9998335], PARAMETER ["Latitude_Of_Origin", 32.5] , UNIT ["Meter", 1.0]]

I ended up finding the ogr2ogr utility and especially with the "peace and joy" promises, I decided to give it a try, I tried this command:

ogr2ogr -update -f "PostgreSQL" PG:"Connection details" 
    "File name.shp" -t_srs EPSG:4269 -nln Table_Name

      

        
        
        
      

    

Now I get the error "Translation terminated prematurely after layer translation failed" - this seems to indicate that ogr2ogr will not be the savior I imagined with an arbitrary arbitrary .prj file in projection 4269.

Any ideas on what to do?