I'm not an official measurer, but I did stay in a Holiday Inn Express last night... With that in mind, and having watched one of my good friends, who is a well-respected measurer, put tape to a lot of antlers and having asked him a question about a similar measurement... I don't think you would take the H4 measurement at those points.
For instance, on the left antler, the G4 and the extra point (not G5) are a ?common base? point. Meaning that there isn't a clear separation along the beam between the two points, thus making it an extra point and not the G5 (think of a figure 8 where the base of the two points touch). So with that in mind the actual mass measurement would be taken at the midway point between the end of the beam and the G4, the same way it would be taken if it were a 5 point with no G5s. Or they could measure the point that comes off of the base of the royal as the beam and the small point on it as the G5, thus taking the mass measurement between those points, and the lower point as an extra. It all depends on what the horn looks like in person.