I think that the answer is simpler and many of us really like the bizarre or complicated explanations, perhaps is due to our glare for the baroque ornaments!!!, LOL
The Queen wore in Canada (1970) the SAME tiara (identical) that wore Sophie (2012), then it couldn't have been reduced (and then increased!, perhaps it will be the effect of some yo-yo diets?) between these dates as stated in The Royal Collection following the error by Fields (why not?, simply because does not make sense at all!!!). If it was bigger when she receive it in 1968, why she reduced it so unsightly (in 1970), if the need for such additional stones not emerge until later (71-73)???
Returning then, please, to the 1st aquamarine gift that she received on the occasion of her coronation in 1953 by the president and people of Brazil and check the stones of this gifts: Necklace, earrings, and then bracelet and earrings, do they have the same amount of stones that was described by Fields?. Where did Garrards all the aquamarines that they need for the 1st design of the tiara (the one with 3 prongs)?, may have been the same source of the gems needed for the 2nd setting (the cathedral/fan thing!)?
I think there are some questions that need to be answered, no?