In fairness to you, Tim, I'll more carefully comment on the particulars here that appear tortured to me -
I've given further thought to this and it forced me to address the following question.
How soon after the Lae departure did AE effect the tank change from 100 octane to the lower octane?
Answer: As soon as possible after becoming airborne.
Eyewitnesses reported the Electra dipping towards the ocean, then recovering. At first I thought that was the Electra coming out of ground effect, but now I think it was both 1st power reduction and 1st tank change.
My reasoning follows:
Since AE had only to clear sea level, it gave her the option of using an efficient and slow cruise climb of 50 - 100 ft/min, rather than a step climb that guaranteed burning 100 octane at maximum rate (60 US Gal per hour?). The reduced weight from the fuel burn aided in the climb performance.
AE had to first reduce power to select the lower octane fuel in order to avoid blowing holes in pistons through detonation/pre-ignition, as well as reduce power to conserve fuel and lean back to 43 US gal per hour.
Having dipped the tanks just before departure, having used a defined period for startup, taxi, takeoff and climbout, having selected away from the 100 octane tank, AE now knew how much fuel remained in that tank especially having performed the procedure on so many previous departures.
That means AE knew how much 100 octane remained upon arrival at Gardiner and also knew preserving that fuel gave her a known running time for the starboard engine once she selected that tank.
Most respectfully, Tim -
Why the urgency to switch tanks so quickly at a very busy and potentially hazardous point in the flight? It gains nothing. A safer approach to your notion of a gentle cruise climb (which is itself something most of us would favor) would be to allow the craft to find a stabilized climb and gain safe altitude, throttling back when safe (and respecting any METO time limits). There would be no urgency to switch tanks - 100 octane would be fine, and there was an ample supply awaiting NR16020 at Howland as delivered by the Itasca.
How much 100 octane would be consumed by using this reasonable conservatism? Assuming warm-up, taxi, take-off and the first 5 minutes of climb to gain some safety margin, all pulling from the 100 octane reserve, would use something on the order of perhaps 10 gallons at the outside (but don't take my word for it, dig into the real numbers and do the math). That hardly makes a compelling point of reaching for fuel tank controls and making a switch on the sea deck just after sailing off the end of the grass runway at Lae: fly the airplane first, gain some comfort margin, then tidy up the long-term needs. That's especially true for single pilot ops in an airplane like the Electra (Fred was in the back - the lady wanted to do it herself).
Your reasoning as to Earhart somehow wishing to preserve 100 octane so as to 'know what was left in tank' (if I follow your logic, in part) seems to be pure conjecture as we have nothing from Earhart suggesting such a concern. Further, the presence of 100 octane vs. 80 octane at the end of the day means nothing because for battery charging: fuel is fuel (perhaps you didn't intend the distinction, but somehow I read it in the sum of your point).
This reasoning is why her focus was heavily on the state of the battery "Watch that battery" rather than transmitting for all they were worth pending an imminent and permanent stopping of the starboard engine due to fuel exhaustion.
Because I agree with Bill de Cleef's 1200 RPM minimum for charging, my estimate is that the 100 octane reserve provided for 4 hours running of the starboard engine at half cruise consumption (21.5 divided by 2 US gal / hour = 10.25 US gal / hour).
You are of course free to agree with anyone's opinion on 'minimum for charging', but the fact is that generator and engine combination have been demonstrated as adequately charging for the purpose we're talking about at around 900 RPM, and with very low fuel consumption - around 8 GPH.
"Watch that battery" was a necessity: no matter how much engine power Earhart applied, the poor little Eclipse generator could only give about 1/2 of what the radio transmitter demanded. The battery would necessarily deplete, even if Earhart were running the right engine at full boost / high power, 100 octane and all.
'Standby' (receiving) was a bit different - the generator could provide for that and battery charging. Yes, higher RPMs would charge marginally faster - but fuel consumption does not increase on a linear scale, but goes up exponentially when one bumps the shiny knobs forward. Patience...
Doesn't some inner pilot instinct tell you 'conserve' when you have very limited fuel and a need to transmit as-can? Watch "Island in the Sky" (written by Gann, portrayed by John Wayne and notable others) for a fair demonstration of the dilemma of transmitting on old sets and power demands: it left shitty choices. Somehow my pilot instincts - which seem to agree with what we know about even Mantz's views, are that the least smelly choice would be, if one could start an engine, to use modest power, 'watch the battery' and periodically make 'burst' transmissions.
If Earhart actually did ever say "watch that battery", then I believe (my opinion) that she was well attuned to these things and carefully managing all that we've discussed. Despite her other shortcomings - ground loops, off course arrival in Africa, radio nonsense, the lady managed to fly a respectfully demanding transport 3/4 of the way around the world without significant mishap - not bad. That take-off at Lae was a piece of fine work by anyone's standard: I'd bet not one man watching that day would have eagerly traded places - it could have easily gone wrong and been turned into a smoking hole. As you rightly pointed out elsewhere of late, tail-draggers aren't very forgiving to bad man-handling.
Her keeping her cool and dropping into ground effect as she sailed off the end of the runway was an impressive move, whatever the reason - and none of us will ever know for sure how expected or not that maneuver was. It might have been a momentarily desperate response to very marginal take-off performance that day (been there with south Georgia pines in the windshield), or it could have been one of those near-joyful acts of conservative energy conservation to gain the best energy state for safety that looks more dramatic than it really is. She apparently handled it well - I don't recall any dramatic report of it from the flying community - just one of those one-off things that turned out well and wasn't too shocking under the circumstances of the day.
I bother to elaborate on all this for the sake of the lady's character and judgment - not out of chivalry, but of common sense: some of her basic stuff was pretty darn sound, and I have severe doubts (my judgment) that she would over-gun the engines in a fuel-limited situation for the sake of overly aggressive transmission times.