Well, yes, and that is how everyone else has taken it. Using your "decimal degree navigation notation" would make the position reported at 0718 Z 4° 20' south, 159° 42' east, 43 SM away from the correct location. (BTW, you are the only person in the history of the world to use decimal degrees for latitude and longitude for navigation, you can find this out for yourself by referring to any navigation text. Just because Google Earth allows people to use that notation doesn't make it a standard navigation notation, Google Earth is not for navigation and it wasn't even available in 1937.)
You are not suggesting that we pull out a map, compass, protractor, and a slide ruler are you? Although Google Earth does display degrees minutes seconds, it seems to only accept decimal degrees as input. Debating over the form of the coordinates is completely irrelevant to the discussion. I also do not see a point in debating whether visualizing in Google Earth is a valuable tool, we are not creating precision navigation plans here, we are talking about 2 points on a map. Are we bound to some secret oath to use old school degrees minutes seconds and nautical miles? If you like it, go for it, I think the conversion is trivial and not worthy of further debate.
The distance from the 0519 Z erroneous position, 7.3° S 150.7° E, to 4.33° S 159.7° E reported at 0718 Z, both positions that you prefer, one hour and 59 minutes later is 685.4 SM making the ground speed 346 mph which is a whole lot less reasonable than the 112.5 mph that you calculated for the ground speed between the correct locations.
Yes, this is why I said the time stamps are problematic and I stated this. It seems reasonable to me that the Lae radio shack was not being run like a well oiled military machine. If it were, we would not be having this discussion. Clearly either the coordinates given are wrong or the time stamps are wrong. For that matter they could be be wrong invented after the fact by a sloppy radio operator that had no idea what was unfolding at the time and had no concept that people would be discussing the details 75 years later trying to make sense of it. There are currently no facts able to substantiate the truth one way or the other at this point.
This modification latitude from 150.7 to 157 was also proposed by the Waitt Institute. Rather than considering that the time stamps could be in error, they also focused on this idea. Is this any more valid than 5:19 becoming 2:19? Maybe Balfour was dyslexic? Who knows. Once you go down the slippery slope of changing the data, anything is possible. I am sure I could find a yet to be discovered set of coordinates that would fit perfectly with the time line with just a couple of digits swapped here or there.
The report one hour prior, where they stated that they were at 7,000ft, is interesting in that it could suggest that they were still approaching the storm, uncertain of a plan to maneuver around the storm and eventually decided to climb up and over at 10,000ft, an hour later. Can you provide a reasonable explanation for the one hour report prior to the 5:19 GMT report?
You also never explained with your line of reasoning why they would continue such a long segment before heading back to the course? Was the storm that large such that they had to go 687 miles out to get around it? Perhaps they were just sight seeing? Waitt never seemed to address that either but it sure pushed that square peg time stamp in to a round hole, hey kind of like a rabbit hole.

And to be consistent, you must also be claiming that the correct coordinates for Nauru are 0.32° S 166.55° E, the same as 0° 19.2' S 166° 33' E (supplying the missing "6" in the longitude that Balfour forgot.) But wait, putting that into Google Earth takes you to a spot 31 SM away from Nauru, see the attached chart, so maybe that doesn't make any sense.
Perhaps Balfour's estimate was pretty good and the telegram operator made the mess. It is obvious from the other typos this was not a professional at the keys. How can you explain that? On balance of the evidence, I would say it was the telegram operators fault looking at the other mistakes and typos. I think that the dropped 6 is just as probable as any other explanation. If the standard practice for this guy was to specify degrees to the hundredths, this makes perfect sense.
Let's run down your theory again about the fractions really being the minutes of the coordinates. 0.32S becomes 0°32'.
What about the .32S? While not completely accurate, it is close. (Me)
To the level of precision attainable in flight navigation, to the nearest minute of latitude and longitude, the position of Nauru is 0° 32' south, 166° 55' east. (You)
So let's compare 0.32S 166.55E to your 0°32S 165°55'E. I think, and I could easily be wrong since I am working with decimal values, that the 0.32S 166.55E produces a 30 mile error while the 0°32'S 165°55'E produces and error of 120 miles. And this was your basis for the other coordinates outside of Lae? I am no navigation expert but the dropped 6 makes a lot of sense and one fourth the error.
It fits a whole lot better than your interpretation of the facts.
What fits better? The square peg or round hole?