While you may convince your supporters ...You are playing to your audience.
Ladislaus has supporters, but mainly those who support truth/evidence. I've never been the science-type, and never cared about space/stars/etc. I only found out about flat earth a few years ago and I only support it because
a) it makes sense Scripturally/theologically,
b) there's tons of historical evidence for it in the ancient world, all of which lines up in most details,
c) the ancient world learned directly from Noah, post-Flood, who would've learned directly from Adam as to the origins/nature of the earth
d) any notion of heliocentrism or the earth being a planet is pagan/occultic/satanic in nature, because it subverts God's order
e) any notion of 'infinite space' and 'galaxies' is a lie, meant to expand God's creation and make earth/humanity/salvation less important
f) God created everything for the purpose of salvation -- we are not meant to travel to the moon, or mars -- but only heaven.
g) Anything in space is meant to glorify God in its beauty, not to be part of a 'unexplored space' which distracts from our obligations to God.
h) All in creation is centered on earth, and anything which expands this notion into space/universe, minimizes the importance of the Church, and Christ's work here, and His continual, awe-inspiring sacrifice in Holy Mass.
i) Pick any catholic chapel where Our Lord is in the tabernacle...THIS is the center of creation...HE is the center of all that is important. Not mars or the moon.
j) God would not create 'infinite space' which is without Him, without grace, without Catholic truth. This is purely a satanic distraction.
k) Philosophically and religiously, the whole idea of an explorable universe is anti-catholic.