Hello giacomo,
That setup sounds sensible.
How bright would you say it is as a function of “the brightest GFP cells you have ever seen”. If it is <0.5% of “very bright” it will be difficult to measure due to other autofluorescence and filter bleed-through. This consideration will depend on what the plasmid copy number/RBS/Promoter strengths all look like.
Also, what OD level are you regulating it at? Something like 0.5 is probably optimal, if you have it very low (e.g. 0.05) then the signal-to-noise may be more tricky as well.