Some notes from the AUSKF Summer Camp that I can still remember. :p They are from Terachi sensei (寺地) from Tokyo Metropolitan Police (警視庁).
The priorities of kirikaeshi are in that order. First it's big and correct. Second is power. Third is speed. And finally it's lightness.
Kote men: Not just speed. Having 'impact' on your opponent. (Like how it feels from Arnold and other sensei.)
Kata
#3 uchidachi: The blocks are more pressure. Don't hit. Keep the hands in the center of the body and tip to shidachi's throat. Slight turn of body as you step back.
#7: Uchidachi's tsuki is to the shoulder level
Uchidachi's tsuki in #3 and #7 is not flat, only slight turn. Uchidachi's tsuki in #4 is flat. #4 is aiming for in betw ribs for the right lung. #3 is the solar plexus, #7 is to the shoulder in an aggressive move to intimidate the shidachi.
#6: While responding to shidachi's pressure from gedan, uchidachi keeps the blade straight up-and-down. Don't turn. There is a brief turn for kodachi #2.