Which variant of GFP do you use in your experiments ? Some variants are dimeric or tetrameric and can cause aggrégates when highly overexpressed.
In your images the green fluorescence appears as big dots but without any scales it is difficult to give an approximate size of these dots.
The size and shape of green dots make me think of plastids, but are sure sure it is GFP rather than respiratory chain factors such as quinones or flavins. On which microscope did you acquire this image ? Can you make emission spectra to discriminate between GFP and others fluorescent compounds ?
Plastids in epidermal cells are etioplasts, not chloroplasts. They are smaller, much more refringent, and they lack chlorophyll.
The fact that this cannot be excited with other wavelengths than 488 is an evidence of GFP. On Zeiss microscope you can have the emission spectrum and you can see if the peak is around 510 nm, which would be another evidence of GFP. As EGFP is monomeric it is unlikely to form aggregates, unless a huge overexpression.
I had troubles with a LaminB-Receptor fusion under the control of a 6x35S promoter. In Tobacco epidermal cells it marked the nuclear envelope, as published for mammals and Arabidopsis, but also reticulum and plasma membrane. This huge overexpression led to an abherrent localization, maybe it's the same in your case.
When you go deeper in the leaf, do you see transformed parenchyma cells ?