Your drawing shows the the ratio of G3 to G1 as 1 to square root 5

If square root of 5 represented 280 royal cubits for G1, then 1 represented 125.2198067 for G3

For G3 the double cubit is clearly important at the base, according to Petrie, and the observed slope is very close to a rise of 56 digits (the double cubit) and a run of 45 digits.

Converting the hypothetical slope to degrees for comparison with survey:
51 degrees 13 minutes

Petrie assessed the slope as 51 degrees 10 seconds, which is close enough.

The area of rectangle shown in your diagram is 2 square units and area of each of the triangles in the rectangle is 1 square unit.

This reminds us of the general formula

Area of Pyramid cross-section x tangent of slope = 1 square unit, if height of pyramid is taken as 1 unit.

We can show that this formula works for G3, as it does for other triangles:

The area of G3 = 125.2198067 x 100.623059 = 1 x 0.803571428 square units

Tangent x area = 56/45 x 0.803571428 square unit = 1 square unit

(because 45/56 is 0.803571428)

Scientifically, we would normally round off at say two decimal places but I wanted to show the mathematical relationship as exact.

Lets now see if your theory fits Petrie's estimate of base side-length:

2 x 100.623059 = 201.246 royal cubits.

If this was the architect's model then the intended base side-length would have been 201 royal cubits 7 digits.

If the length of the royal cubit was 20.61 inches plus or minus 0.02 inches (as indicated from G1), and the base was built with a precision of 99.9% (1 part in 1000) as a mean, then the mean side-length should be:
Somewhere between 345 feet 0 inches and 346 feet 4 inches.

Just let me find Petrie's survey again ...

Mean Side length = 346 feet 1.6 inches

In my opinion your geometric theory is consistent with the facts, but is not proved by the facts.

I am not aware of any other theories that fit the facts

Mark