An eightfold or ninefold increase over 1800, it is estimated that

(A)over 1800, it is estimated that in the course of the nineteenth century eight or nine million square miles of land were settled in North and South America and Oceania
You could argue what does 'it' refer back to, has no reference , however this juggernaut plays hell lot of roles where in here its not acting as a pronoun but rather used a tool to state a fact , the sentence structure and meaning is fine therefore let us hang on to it

(B) over 1800, in the course of the nineteenth century, it is estimated, eight or nine million square miles of land were settled in North and South America and Oceania
i guess there is no real reasoning to eleminate just that A better conveys the meaning therefore ..........-------->

(C) over the number in 1800, eight or nine million square miles of land in North and South America and Oceania were settled in the course of the nineteenth century
what number ??? can we summon anyone or refer back to no .......so kick it out

(D)over that of 1800, it is estimated that in the course of the nineteenth century eight or nine million square miles of land in North and South America and Oceania were settled
now 'that' is a problem what exactly is it latching on to no clue , clear cut reasoning to eleminate therefore out

(E) over the area occupied in those regions in 1800, an estimated eight or nine million square miles of land were settled in North and South America and Oceania in the course of the nineteenth century.
'those ' region please DM me if you get any idea exactly it's intending therefore out

THerefore IMO A