I don't think using the word "flat" is a clear way to convey the historical Catholic understanding of the earth, no matter how much one qualifies it.  Catholics of the past used the word "sphere" and I think that we should too.

Some Catholics did use sphere, but not all. 

Samuel Rowbotham, a science-based observer of all things regarding earth, was born in the 19th century, quite a bit prior to Eric Dubay.  No Catholic takes much time with that little pagan, 

In 1856, Rowbotham married for a second time and had two children, one of whom died in infancy. In 1861 when he was 46, Rowbotham married a 15 year old girl (with whom he was living at the time of the marriage) and settled in London, producing 15 known children, of whom only four survived. He was named in numerous cases of wrongful deaths, including a "death by misadventure" for accidentally poisoning one of his own children. He was named responsible for other deaths using his quack cures of phosphorus. He was also alleged to be using the name "Dr. Samuel Birley", living in a beautiful 12-roomed house, selling the secrets for prolonging human life and curing every disease imaginable.^[6] Augustus De Morgan refers to him as S. Goulden.^[3] He patented a number of inventions, including a "life-preserving cylindrical railway carriage". He is not known to have held any medical degrees and his professions are named at different times "chemist, physician, journalist, soap boiler".

Samuel Rowbotham, a science-based observer of all things regarding earth, was born in the 19th century, quite a bit prior to Eric Dubay.  No Catholic takes much time with that little pagan, except for where the science cited assists in discerning truth. Just like Thomas Aquinas and St. Augustine probed the minds of pagans like Aristotle and expounded on their writings to verify Catholic teaching.  Truth is truth no matter where it's found. 

Yea, he was a Prot.  Still, his scientific acuмen has merit independent of all that.  Again, like Plato and Aristotle. 

I agree. Truth is truth no matter where it is found, since even pagans can sometimes discern the Natural Law.

Yea, pagans can see natural truth. We still need to be careful about research, mistakes are easy to make. I also rely on other clues independent of particular source. Like the checklist for each model. For instance, I cannot ever find anything of substance in the globe model, no verifiable facts, no repeatable experiments, no support from scripture, nothing reasonable. They have curved water, the illusory vacuum of space, fake astronauts, ridiculous "proofs" like the coreolis effect, they deny the horizon, deny sea level, deny the firmament, or at least attempt to explain those things away.  Flat earth information can be elusive, but not having all the info does not affect the info we do have, all of which makes way more sense than believing there are upside down people on the other side of earth.   

You are still missing the problem with all of the descriptions.  When you say "sphere" are you talking about

1) the shape of the physical land/terrain? 
2) Or are you talking about the shape of the physical land + atmosphere?
3) Or are you talking about the shape of the physical land, when viewed from above (i.e. looking down from the heavens, viewing land like a map)?
4) Or are you talking about the shape of the physical land + atmosphere + what's below the land (i.e. inner core)?

Most people that i've run across use "flat earth" to ONLY describe the physical land mass that we stand on.  They aren't talking about the atmosphere or the shape of the earth BELOW the walking-surface (i.e. inner core).

Based on my limited knowledge, the old "sphere" description is based on a side-view of the earth, including 3 things - physical land + atmosphere + inner core.  Like all the pictures that DigitalLogos posted.  That is a "sphere" shape of the WORLD, which includes flat land.

Conclusion:  The modern-up-to-date description of the old, catholic, view should be re-named something like:
a) (viewed from the side) Sphere-shaped world, with a flat land terrain
b) (short expression) Sphere world, flat land