I think there is a problem with the way you are thinking about the whole thing.
To sum up:
You use Cesium points which are from a Digital Elevation Model. Those points are expressed in WGS84 and the height representation is ellipsoidal height
GPS gives you height which is ellipsoidal height
You have geoid height from the EGM2008 model
So when you ...
Disclosure: I work for Esri as a Sr. Product Engineer specializing in coordinate reference systems and transformations.
I believe the use of this sphere is specific to the QPF data and not in general usage by NOAA. For instance, National Geodetic Survey is an agency within NOAA and it doesn't use the spheres at all.
If you have access to ArcGIS, try ...
I think the data's in the Philippines. Is that correct?
The latitude, longitude values are in DDMM.mmmmm, packed degree-decimal minute values. For example,
3020.13221706(latitude),N, = 30° 20.13221706 = 30.00220361767
12118.46433560(longitude),E = 121° 18.46433560 = 121.3077389267
This is confirmed by several sites like this one.
What you will need to ...