I can't speak to the hawkeye, but I have the other cyphastreas that you listed and I am getting good growth under LEDs.
Mint Cyphastrea - I have this in my kids' tank which is basically actinics with, at most, 20% whites. Equivalent is probably low in the tank where it would catch some indirect light.
Pepper mint Cyphastrea - low in the tank... grows like crazy
Bling bling Cyphastrea - I have mine more towards the middle of the tank, also grows like crazy
Lime green Cyphastrea - same as Bling Bling... I've found the new growth to be purplish/brownish initially but it eventually colors up
Brick red Cyphastrea - I had this in low, partially shaded, light and wasn't seeing much progress so I recently moved it to an area that is still toward the bottom of the tank, but directly under the LEDs with nothing else shading it. Growth has really picked up, but the color in some areas have washed out a bit, so I may need to find another spot where the lighting is not quite as intense.
In my experience, if you are seeing the colors on established growth wash out then it is probably under too much light. For most of my cyphastreas, the new growth colors initially are fairly drab, but eventually the colors improve. Exceptions to that have been the Bling Bling, Mardi Gras (when under stronger light), and JF PPE.