Hi. I really don't have expertise to help you, but I'll throw in some ideas in case they stimulate any good thoughts.
You might check out alternate promoters to see if there is on that shows more constitutive robust expression. I don't know if SV40 or EF1a might work better, but you can research alternatives (if you haven't already). Could an inducible work better, or does that just complicate it?
Or, perhaps you would have more success if you try different transfected cell lines. Maybe the methylation Crsn mentions wouldn't occur if the same gene construct integrated into the genome at a different location. After all, the cells must express some proteins. The right promoter in the right locus would have to work. What if you did the GFP transfection, put the transfection cells onto your scaffold, and then later sort the cells to select for cells that express the most GFP in your experimental model, and create some cell lines from those. Oops: am I not allowed to use immortal cells? I see, you start with a transgenic rat. So, in this case I must mean you might have more success with trying different transgenic rats, even if derived from transfection of the same GFP construct, because descendants of different founder transgenic rats will have different integration sites, and copy number at that locus.
Instead of a simple transgenic, the gene might be knocked into a locus/gene known to express in fibroblast/ligament tissue, so the normal methlyation/etc. at that locus would be know not to interfere (hopefully).
Maybe in situ hybridization or PCR might find the genomic GFP in the sections. Oops, I guess FISH is an in situ hybridization, but I guess you can compare other chemical or radioactive probes, and PCR can amplify the signal, if it can apply to your size and situation.
Well, I'm obviously no help, but maybe this will stimulate an idea in someone else.