Wow. A lot to unpack there. Let's stick with the short answer.
Galleys, as the linked Wikipedia article show, were mainly rowing ships. They worked in the ancient Mediterranean because of A) Slave rowers, and B) Relatively little rough weather. Galleys don't handle a lot of chop well.
If you want more of a sailing ship. Take a look at viking longships or chinese junks for pre-gunpowder ships designs.
Truth is, galleys were about the only ships that ever widely used things like catapults. Masted sailing ships have too much rigging to get in the way. But this is a game, not history!
_________________"Bighara RULES!" -OgrepuppyKelvernia
- My DCC campaign setting at Obsidian Portal