Here, here, it's not the art, it's the artist.
However, in regards to cross-training: If while building your house, you change the construction of the foundation on advice of neighbors, you will not have a strong house because it rests on a weak foundation.
Okay, okay. I know what I'm talking about. I just don't know how to say it
I'm sure someone else knows this one. So please, throw me a line.
Also, Shioda Sensei, in his book "Shugyo: Harmony in Confrontation" says that it's those who work on timing that you have to worry about. I'm not 100% sure, but it seems like you'd be more busy learning new techniques than working on timing.
Finally, since technique is supposed to be reflexive, seems like you're divided. My experience was consistently using the Isshin-Ryu vertical fist for my atemi while cross-training.