Need help understanding Dragon Cohort and Dragon Rider (DLCS)

[Max Caysey]

So, I would like some help understanding how The Dragon Cohort feat (Draconomicon) and Dragon Rider PrC (Dragonlance Campaign Settings) interact. Both feat and PrC reduce the effective ECL of the dragon by 3. Could combining the two actually reduce the ECL by 6?

Like, if you already have a dragon cohort by virtue of the feat and then gain levels in this prestige class, could you then use your dragon cohort as your dragon utilizing the further reduced ECL - thus allowing for a stronger cohort?

Cheers!