Let me preface my reply by mentioning that I am not an end user I am a manufacturer so all my information is based on theory not real world practice.
Your problem is not colour balance - it is the amount of the visible spectrum that is present in the light from the fluorescents referred to as CRI (Colour Rendering Index) or TLCI )Television Lighting Consistency Index). Lighting for image capture needs a CRI of 90 or above and/or a TLCI of 85 and above. This means that you should not need to do anything in post.
Retail and domestic lighting can have as little 70% of the visible spectrum (CRI 70) and this is why it is not suitable for image capture. The human eye is very sensitive to green and so lamp manufacturers often increase the green spectrum as that makes the light source appear brighter.
However the camera simply records what it sees and will notice the higher green content of the light.
This is what causes skin tones to look bad - no one likes to be slightly green.
In my opinion adding +green to your other fixtures will simply make this worse.
You could add -Green to the fluorescents but if you want them in shot this is not an option.
Swapping them out for broadcast quality tubes is the answer - not only Kino but GE Cinema+ or Osram Lumilux Deluxe would be suitable.