OK, I've had a beer, so I'll give it the old college try...
The 4 stops over gambit was not just for any particular shot, but for the entire film. As he states, he shot the film essentially at ASA 12 and processed the negative normal. The lab then had to really ramp up the printer lights to print through the dense negative and a byproduct of this was a desaturated image overall.
As posted above, Hall shot the "color transformation" scene above at golden hour, where the sunlight passes through the thickest part of the atmosphere (in relation to the shooting location), which naturally give the light a golden color. The raking light, along with the pastel color scheme of the sets, produces a near Sepia look naturally, but when the camera position pans to take in the blue mountains, color naturally becomes more emphasized (as pointed out in the interview in post#16).
Now I am sure this natural effect was augmented by the color timer.
The Timer would have probably take the shot, established the light values for the head of the shot in RGB color points to mimic Sepia, wound down to the end of the shot and established the tail of the shot in other RGB color points to what look was desired and then did a color balance ramp from the first RGB values to the end RGB values.
This undoubtedly cost the timer a good portion of their hair and several bottles of antacid, not to mention at least a week of intense testing. It would not have been a linear, cross-fade/ramp between two values, but more of a "modulation arc" between portions of the image to make it look correct to the viewer. A green horse would not work, right?
I do this a lot with the B&W films I time, but I am only dealing with unity gain values of RGB, because... well it's B&W and equal values of RGB equal white light in varying densities.
I don't know what other timers call that, but I call it "ramping".
Just as a still photographer has to do, I have to fit the desired image density range into the print stock by manipulating the density to fit the gamma response, only my targets constantly change.
I cannot tell you how many ramps I had to do when I timed a show print of "A Touch of Evil" by Orson Welles and cinematographer Russell Metty. Blazing lights into pitch black rooms... it was fun.
Motion picture printers (most) use a system called the Peterson Light Valve system of 0 to 50 points of light in each Red, Green and Blue Channel. Like a color enlarger, the tungsten lamp is split into RGB via dichroic mirrors BUT each value has a light valve that can vary exposure in these 50 point values.
Each printer point is 0.025 transmitted lux and there are 12 points to a stop, so you have about 4 stops of independent RGB you can manipulate. (Think of this as turning the dial on a dichroic head, only making the change at 3/10,000ths of a second.)
The printer also utilizes "trims" which is another light valve that intercepts the light as it exits the lamp house before the light is split into RGB by the dichroic mirrors and has the ability to modulate the overall light by 24 points. (1 trim = 1 point) This is more of an overall adjustment that allows the timer to move the entire "envelope" of the 1-50 points within the 24 point range to match dissimilar film stock emulsion batches.
(There are also provisions for ND and additional Wratten filters to make minute adjustments per channel, but we are getting off into the weeds...)
On the BHP Panel printers we use, I am limited to changing point values no sooner than every 4 frames to allow the light valves to recycle and get ready to change. This may not sound very fast, but remember that the film is speeding past a 4 perf high film gate at 100 feet per minute.
So long story short, in my opinion, this was a combination of natural light with judicious timing corrections deftly applied.
With the ability to radically change RGB values, 4 stops up and down in each channel, and the initially over-exposed, thus de saturated image, all of your questions could (possibly) be answered.
