Running a *.jsx file via C# can be done with the Photoshop.ApplicationClass.DoJavaScriptFile(filePath, argsArray, debugModeInt) command.
You can technically pass a *.psjs file into that command and it will run, but the argsArray becomes mangled/corrupted on the way through.
Is there a better method available for running UXP scripts? I cannot find the docs for the ApplicationClass object anywhere online.