I believe the usual process for installing an Elite KBG is to RoundUp the entire lawn and start over.

Does your back yard face south or west? Could be a simple water quantitiy/depth issue. How long are you watering the two yards and how frequently?

Are you going to be happy with the results? Overseeding into an existing stand will result in a hodgpodge lawn of different shades, textures and growth rates. A complete reno may be your best recourse.
For best overseeding results: Scalp the lawn. Run a verticutter over the lawn and rake up the debree. Spread your elite KBG seed and then run the verticutter set at a 1/4" depth over the lawn twice at 45 degree angle to each run. This will cause almost as much damage to the lawn as a complete kill and reno, but will result in very good germination of the new seed. Optionally topdress with peat moss. Drop a starter, water appropriately and mow carefully to keep any surviving extablished grass from out-competing the new seed. Good luck.