What are Some Methods of Handling This Lighting Situation?

How far off of daylight are the florescents?  Some will be green, while others are fairly close to daylight, and some are warm, like incandescent lights. If they are daylight-ish, see if you can get the incandescents turned off. and shoot on daylight WB. If not, then you may want to add a studio light or two on stands to bounce off the ceiling to create your own "ambient", and use a speedlite with a mod for fill.

At night, with no day light, have them choose between florescent and incandescent, and gel your flash to match.

Avoid bouncing off the green wall as much as possible. Some light will bounce, but don't sweat just a little color cast, that's how your eyes would see it if you were there.

Or shoot black and white.

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