The Limitanei being able to absorb so much more arrow fire is coming in clutch here. If this was ordinary spearman, this would be slightly more beneficial for Beasty. With Limitanei you can just hold off the Keshik so so well.

If your critical resources are next to each other, Byzantines need to commit harder to secure them, and Mongols can deny that faster because of double spearman production in dark age.

Even with the Hippodrome, you do not want to trade your horsemen into Keshiks.

Maybe neglect the Hippodrome and go Limitanei and Longbow, because if wood is a problem for Mongols, they can't solve Limitanei at all.

Longbows don't trade well against Keshiks, especially when Keshiks have +1 ranged armor.