Andrew... try my Split Layers by attribute
http://www.arcgis.com/home/item.html?id=15ca63aebb4647a4b07bc94f3d051da5
It is a convention toolbox, which you load in ArcToolbox and run it from there, not ArcCatalog.
Porting it over to ArcGIS Pro and File Geodatabases is ongoing. Now let me know if you can get to that link...it isn't visible from ArcScripts 2.0 Beta for some reasons that are too difficult to explain.
In any event, you can split your big file into subfiles, based upon a common attribute...which I presume is a District field in your table. If you read carefully, you will get outputs that are separated. Cavaets, the inputs must be a shapefile (long story) so export any featureclass to a shapefile and process all your results in a folder. This will produce a number of unique shapefiles which you can bring in as feature classes as you need them, or simply create a file geodatabase solely for this purpose and load the stuff up...do your processing and the rest of your projects are intact and undisturbed. Let me know