Sengoku get handcannoneers in castle age. Ottomans also get handcannoneers in castle age. The Janissary does bonus damage against all sorts of cavalry while the Ashigaru handcannoneers from Sengoku only do bonus damage against heavy units like a crossbow unit.

When facing a mass infantry composition like samurai and spearmen, you should only use the melee armor aura on the Mehter because it gets too much value.

With a critical mass of Janissaries and the Mehter's attack speed aura, they can one-shot mounted samurai and fire rapidly.

The military school opening allows Ottomans to slowly apply a little bit of pressure onto those Yatai.

Sipahi are a natural transition. They're not something you're wasting resources on just to respond to the Yatai because you can use them for anything and everything.