Getting wonky elevation readings, even after post-processing

I tested it with my own coordinates and the geoid program is of by 1,5m . So its not entirely correct.
How accurate the calculator is depends where you are located.
Also notice the difference between ellipsoid height, geoid height and orthometric height.

Your ellipsoid height is basic start for any calculation of height. This guide is usefull too Placing the base | Reach RS/RS+

1.I havent seen any way rtkpost can process orthometric height yet.
2.I think mobile topograher gives a better geoid conversion on the fly at the moment, it also saves each point as you wish
3. if not you can postprocess it to a .kml or .gpx file and open it with qgis.
But i havent had any luck getting qgis to work with other height models. Ref this thread

Got a tip to creating your own projection and reproject layer to it. Not got around to do this yet