Additional range from the Temple of the Sun on Nest of Bees can outrange longbows, negating their range advantage.

Zhu Xi has no access to regular archers, which is what you want against longbows. Zhuge Nu are not effective against them, so they can't fight Byzantine longbows in feudal age.

Enough Cataphracts should beat the lancers even with the Dali Horses attack speed upgrade, as long as they are backed up by longbows.

Byzantine Royal Cannons are superior to Zhu Xi's bombards: three can one-shot a Nest of Bees, and they have more range.

Limitanei are exactly what Zhuge Nu will do very well against.