I'll speculate that two factors possibly helped BHG in their development cycle. One: BR was already working on RoN before leaving Firaxis. I can easily imagine that BR wanted to try some RTS game and then Sid came and said "Brian, you're going to work on Civ3". And Brian decided to leave shortly thereafter, carrying with him some sketched form of the game.
Two: while BR was in Firaxis working on RoN, he used the Age of Empires engine to give form to his ideas. After he left Firaxis, he then called Microsoft and said: "hey, I've got this cool idea of a game that uses the Age of Empires engine, what do you think of publishing it?".
DISCLAIMER: all the possibilities above described are mere speculations that do not intend to reveal any truth about what really happened. Plus, my words are backed by nuclear weapons.