I have owned the F3 for almost a year now and there is a lot to like about the camera. However an area where it still does give me issues is when shooting in florescent environments or through windows jelled with ND. In Both cases I find the camera sensitive to green and hard to balance cleanly.
When shooting in florescent rooms I usually use kinoflows and or Divas to light my subject and either white balance out the green in the room first and then match it with a filter pack on the lights of plus green, or use the white balance preset and use the matrix to try to dial it out. In both cases it is very hard to get a clean looking background with clean white walls and true color on the subject. The same is true for lighting an interview against a large plate glass window. For this I usually jel with 1.2 ND and key with a small HMI like a joker. Again I find the background picks up a green cast and I have to add 1/2 plus green to the key and it is hard to make look perfect either white balancing or using the presets. In both cases when white balancing I usually resort to the old trick of white balancing through 1/8 green and 1/8 or 1/4 ctb other wise the image looks cold.
The strange thing is that my assistant often shoots 2nd camera of the same scene with a Canon 5D or 7D and the image is easily made clean and free of green from the get go with out having to add green to the key light and my client usually likes the Canon image better.
Does anyone have any suggestions on how to better handle these situations?
You might try adding a light pink or magenta filter to the camera. Do this after you set your white balance. We use to color correct this way when doing "old fashioned" photography under florescent lights shooting ektachrome film! It would be interesting to see if this works.