In general, the advice we give is that transferring between PhD programs is both costly and difficult. BGSE is very reputable; if you got a master's in econ from there but didn't get into one of your target schools, I have some skepticism that your next 1-2 year of grades at your Greek PhD program will substantially change your chances. People might still rely on the BGSE grades as their main criterion, because they can directly compare you with other applicants they're considering from BGSE.
This advice might not apply consistently in Europe because some PhD programs only last 3 years, so they might be willing to take chances on a student with good research fit . Maybe some European forum members can chime in if they know of any such cases of transferring between European PhDs. In any case, for your transfer to be taken seriously, you should try to get a very strong letter from the professor at your own PhD institution, hopefully with an explanation that focuses on research interests rather than ranking. For this purpose, it may be good to focus on RA work with a well-connected member over your classes (it's difficult to excel in both things at the same time); but you'll need to figure out the balance yourself.
I think it's unlikely you'll get more specific advice from this forum. I only remember one Greek member, and it's very hard for us to give accurate advice without related experience.