Stratiotai are post 4th crusade kataphractoi/lancers.

Tagmata were an evolution of the Comitetenses and Palantinae forces. They full time soldiers stationed around Constantinople. Each was about 4000 (on average but the varation was given as 1000-6000) strong. There were about 6-8 each of cavalry and infantry. I've read 3 articles about and each translated the name "Tagmata" as a different modern formation. Battalion, regiment, and brigade were all used. I'd use regiment or brigade personally.

As for Pronoial ailagion I think that much like the schimitar swinging tunic wearing byz-inf from MTW they tossed it. But the description of the new Byz-cav ascribes those men as having pronoial land grants, the new byz-inf too.