The significance of discovering the truth should include writings of all the Fathers and saints because there are contexts like Basil's statement that do not reflect the questions involved. Can we dismiss everything based on one statement? Also, St. Augustine leaned heavier toward flat earth than the globe, as well as other Fathers who describe a flat geocentric earth. It is definitely true that science is an important consideration because people ignore the subtleties of the discussion: That a firmament dome is inconsistent with a globe and a millions of miles away sun. Dismissing clues is common among those who've made up their mind to accept the heliocentric model but then, that won't necessarily reflect the truth.
The majority of scholars consider St. Augustine to have believed in globe earth and that is my own impression from reading various passages. There is one major Augustinian scholar who claims that he believed in flat earth. The reason it is debatable is that Augustine did not make any direct statements on the issue. Because he did not think it had any spiritual significance.
There are, at most, five Fathers who wrote about the earth being flat. Some of these statements are ambiguous. There are perhaps two of them that are clear. The idea that there is support for flat earth among the Fathers is an exaggeration, originally promoted by anti-Catholics to discredit us.
St. John of Damascus wrote a summary of the teaching of the Fathers which, coming from a Doctor of the Church, is a highly credible source. He said that some Fathers believed the earth to be flat, some believed it was a globe, but that it is a matter of no significance.
Personally, I don't care much about the shape of the earth either. My interest in this subject is that I do not want to see Church teaching misrepresented. I don't care if you think the earth is flat. Just don't say that this is a Catholic teaching or that it was the consensus of the Church Fathers.