I read some of your other thread:
The Arduino IDE doesn't seem to have a problem finding the .h files since it opens them up in separate tabs with the sketch window automatically when I open the sketch.
This means they are in your sketch directory. In this situation you must use quotes, i.e:
#include "MySketchDirFile.h"
Brackets: '<' and '>' are used to specify common files, or in the IDE's case files that are accessible to other sketches.
#include <LibraryHeader.h>
The IDE does non standard things which enforces the use of <>.
When compiling the IDE copies your sketch files and any other files specified in '#include <>' to a temporary folder for compilation.
So ensure all libraries are included using <>, and even more so, you must include any libraries that your libraries include ( strange I know ).
This is to ensure that the files your libraries use are copied to the temporary directory.