> "The teachings of the Church must not be undermined by heliocentrism or evolution research, so findings in those areas will be strictly filtered for heresy before publication."
This is actually a bit of a historical myth that due to anti-religious bias prevails widely.
Contrary to widespread belief, the works of Charles Darwin were never on the Catholic Church's Index of Forbidden Books, nor did the Catholic Church ever state that Evolution as a theory could not be believed, but rather emphasized that a few specific theological events (a garden in which man fell) must remain, though the lead-up to those events was not rigidly defined. This is also why a Catholic priest is responsible for the Big Bang theory.
As for heliocentrism, this is also baloney as it was initially proposed by Nicolaus Copernicus, who was not censored for his beliefs[1], and also served as a Catholic canon (religious member but not necessarily a priest). This idea was backed by Galileo using astronomy, however, Galileo was tried for writings other than his heliocentrism that were arguably heretical (including attacks on the Pope within his work) and not necessarily for the heliocentric view itself, as seen by the Church making Copernicus mandatory reading in some universities for astronomy courses.
[1] The Roman Inquisition would later censor it for a short time, however, their main requirement was that it definitions be changed from fact to theory, and the Roman Inquisition actually used 13 mathematical arguments of their own from the astronomer Tycho Brahe, versus only 4 theological ones. The Spanish Inquisition never censored the book. Even though Brahe was later proven incorrect in his arguments, he was still one of the most accurate astronomers of the era, and Johannes Kepler (of the Kepler Space Telescope fame) would later use his measurements to create the 3 planetary laws of motion. In any event, it would appear that this censorship of Copernicus requiring revisions before publications was due to Copernicus' overconfidence in potentially erroneous mathematics, rather than a theological dispute.