It turns out I dropped out of Stephen Baxter's "Ultima" too soon (I kinda bounced off the absurdly low-tech interstellar ships of the Space-Romans), before he _really_ turned up the crazy: not only is the Space-Roman Empire more vigorous at interstellar colonization than our timeline is, but in the third timeline visited, the Incas beat them all hollow:
"the protagonists reach an alternate timeline where the Inca have taken over the world and set about strip-mining the entire Solar System and colonising the galaxy. Everyone not directly involved in these projects lives on a vast cylindrical space station orbiting the Earth. The space station, by the way, required so much raw material to construct that the Moon was entirely used up. Several butterflies lead to this. Firstly, the Roman Empire is persuaded to invade Germania rather than Britain, which leads to a Roman Empire that can afford to send colonists to South America with firearms in the 10th century. Then, a volcanic eruption causes bad harvests which weakens Rome to the point that the colonists are left to fend for themselves and intermingle with Amazonian natives. Inspired by Chinese travellers to the New World, the Inca expand eastwards, discover these Roman remnants and go on an eastwards journey of conquest until they return to the Pacific, having taken over the entire planet."
Modern Mayincatec Empire - TV Tropes
"the protagonists reach an alternate timeline where the Inca have taken over the world and set about strip-mining the entire Solar System and colonising the galaxy. Everyone not directly involved in these projects lives on a vast cylindrical space station orbiting the Earth. The space station, by the way, required so much raw material to construct that the Moon was entirely used up. Several butterflies lead to this. Firstly, the Roman Empire is persuaded to invade Germania rather than Britain, which leads to a Roman Empire that can afford to send colonists to South America with firearms in the 10th century. Then, a volcanic eruption causes bad harvests which weakens Rome to the point that the colonists are left to fend for themselves and intermingle with Amazonian natives. Inspired by Chinese travellers to the New World, the Inca expand eastwards, discover these Roman remnants and go on an eastwards journey of conquest until they return to the Pacific, having taken over the entire planet."
Modern Mayincatec Empire - TV Tropes