Sounds like a completely scientific theory if the death of one person over 130 years ago stops all progress on it. I'm so glad you're such a free-thinker and not a sheep following a 130-years-dead person like ... oh, wait.
In all honesty, this age of inter-connectivity surely could bring a study of the continents together! What a golden opportunity to build a real FE model than today?
Samuel Birley Rowbotham was a rich medical doctor and proprietor of pharmaceutical company. We have nowhere close to the resources the original society had.
Members of the original Flat Earth Society (then called the Universal Zetetic Society) had enough resources to publish monthly 300+ page journals of their studies, write numerous books, and engage in debates at universities all over Britain on the subject. At one point there was even an entire city in Illinois where Flat Earth Theory was taught in the schools.
They had a bigger budget and better funding, which trumps any "modern" conveniences.
Modern conveniences like web cams on every continent, weather balloons that can carry digital cameras, world-wide communication, CAD programs where you can draw 1:1 real-world scenarios, free ways of publishing online journals, images of every coast known to man... Yeah, we're really lacking compared to the golden age of the 19th century.
The 19th century had all of that. It just cost more.
Webcams on every continent = People on every continent
Weather balloons with digital cameras = Hot air baloons with people on them
World wide communication = Hand written letters
CAD programs where you can draw 1:1 real-world scenarios = Trial and error with building physical materials
Free way of publishing online journals = Traditional academic journals
Images of every coast known to man = Worldwide exploratory and surveying ships
Modern conveniences are just that - conveniences - nothing more.
Webcams on every continent = People on every continent (But with webcams you can personally view multiple parts of the world simultaneously and not have to use unreliable eye-witness testimony)
Weather balloons with digital cameras = Hot air baloons with people on them (It is much much easier, safer and cheaper to send a weather balloon up to 100,000 feet that a human)
World wide communication = Hand written letters (Again, instantaneous communications rather than the months it would take to get a letter from say North America to Australia)
CAD programs where you can draw 1:1 real-world scenarios = Trial and error with building physical materials (CAD sounds orders of magnitude cheaper to use)
Free way of publishing online journals = Traditional academic journals(Instant access to larger amounts of content since we are less reliant on mainstream or othodox publishers, a double edged sword)
Images of every coast known to man = Worldwide exploratory and surveying ships(Again, the savings in time, money and safety is incalculable)
It does not seem like the modern tools available are just conveniences. I think if you create a systematic way of using them, that you can do more work for less money and time than you could in the 19th century.