do you have any evidence to back up that assertion?
if you look for it, you'll find this instead: that a flat earth was only popular for a very brief time amongst a minority of people in europe. it was a fundamentalist religious belief, not a popular science. a scientific conviction and/or basic belief of a round earth goes back to almost all ancient cultures that we know enough about to know their round/flat beliefs.
Afraid not. You're right in thinking that the modern, western Flat Earth movement was born with Rowbotham's UZS (looks like someone's been reading Garwood's FE:HoaII by the way- good work if you have).
You're wrong in thinking that FEers have historically (and we're talking broadly historically here) been a minority.
Of the Seven Sages of Greece, every single one was a Flat Earther. In fact, I'd put money on it that every pre-Socratic scholar you can dig up held Flat Earth beliefs. Even with Plato's whackjob globularism, it's likely that the vast majority of ancient Greeks retained zetetic worldviews. We know that the ancient Egyptians were aware of the true shape of the Earth (don't have time to source this right now - trust me, they were), and theirs was one of the most successful ancient civilizations in history.
Medieval western science is where things start to really go wrong. You'd be right to claim that many Europeans from 1000 to say 1800 were Round Earthers - the same scientific scrutiny that bought us the idea that the human body is filled with nothing but blood and bones, and is governed by four magical "humours", resulted in people taking Platonism on Earth's shape seriously. Newton and fellow enlightenment buddies are the ultimate culmination of this bogus science.