Hi @jcmichelsen1​ , since FME supports reading GPX format and writing AutoCAD format, I think you can create an FME workspace to read features directly from the GPX file, validate them and then write them into an AutoCAD dataset.  See also these pages to learn more about the reader/writer.

GPS eXchange Format (GPX) Reader/Writer

Autodesk AutoCAD DWG/DXF Reader/Writer

I agree with @Takashi Iijima​, you can take out the step where you save as KML from Google Earth, that's not necessary. In fact, you may even find that doing your visual inspection in the FME Data Inspector is a good alternative (but it depends on whether or not the freely available base maps are suitable for your purpose).

I would also add that you can build your validation and inspection directly into your workspace. If you are always collecting data in the same geographic area (eg. city), you can set up the workspace to verify that all your GPS coordinates fall within this area. Also, in addition to the AutoCAD writer, I would probably add an HTML writer for visual inspection as well. Using an HTMLReportGenerator, you can create a basic webmap showing your GPS points against a background map like Esri's imagery. This then gives you a quick map to pull up to visually inspect your data.