The answer to your question would be that the sentence that uses a formal style and tone most effectively is the following one: The campaign for women's suffrage began in the 1830s, but it was not until the start of the 20th century that the movement truly took hold.
This is the case because the sentence is a fact without any kind of subjective opinions (such as the second and third options: "I cannot believe", "it is preposterous and shameful") and it does not use a talkative oral style (such as the first option: "the process of redefining the British political nation seemed like it got dragged out).
The campaign for women’s suffrage began in the 1830s, but it was not until the start of the 20th century that the movement truly took hold. Sounds more formal because it doesn't include a opinion and it doesn't include words that weren't cited from people there in that time.
