At a guess - I'm at work so can't check, sorry - you could try 2 methods, both requiring that you edit export_descr_unit.txt...

The first is to remove the attribute of general_unit from the east generals cavalry early unit stats. This would leave only the later general units for the Eastern factions of Armenia, Parthia and Pontus.

The second would be to copy the unit stats for the east generals cavalry from soldier down to stat_cost and use them to overwrite the same fields on the early general. This would get around any possible problem of the game perhaps requiring a early and late general. Or perhaps do this but tone down the stats so that they're not overly unbalanced at the beginning of the game.