As I see it, you are not on the determining end of this proposition. The announcement of the repair extension program says under what conditions the repair will be performed at no charge to you. If your machine fulfills them, it will be fixed at no charge to you; if not, you will be informed and given the the choice to have it repaired at the offered price, or to forego repairs.
In some cases Apple has refused to repair a unit for free because the optical drive has been replaced by a hard disk or an SSD, this despite the fact that no soldering was involved. What do you think Apple will say about your new GPU chipset? 500€ - 140€ (assuming Apple refunds the cost of the chipset exchange) < 500€, isn't it? If I were you I would definitely apply for a reimbursement, whether or not I subsequently tried to get Apple to fix the machine.
À propos having Apple fix it: Bear in mind that people stumble upon this thread because they have a problem, and once their problem is solved, they tend to disappear. So, yes, some people have reported having their MBP's repaired multiple times under the program. But how many people have had theirs fixed just once, and it's still running fine? In order to derive that information from this thread and test your impression that most, if not all repairs, are failing, you would have to read all the postings after the initiation of the program and tabulate how often each poster had his/her machine repaired. And even those numbers might not be representative. Some "lurkers" might have read about the repair extension program here, taken their machine to Apple, got it fixed, and after that experienced no more video issues ... all without even posting here.
When I had my MBP 17" repaired in February I was told that the replacement board was "revised," i.e., not the same as the original. I am assuming that the revision is supposed to address the video issues, either directly or indirectly. At any rate, I have experienced no video issue since the repair. As one contributor to this thread has reported, even on these boards used components are used if Apple deems them up to specification, but the boards as such have never been in another machine. So it would seem that these are not the original boards, and there would be some reason for those so inclined to hope for a "permanent" fix.
However, nobody can guarantee that the next repair for the video issues will be the last one you need, and so you'll just have to decide whether you want to have the chip set exchanged again, or try Apple. Apple has been offering to exchange machines that resist three or four attempts by Apple to repair them, so this might be one reason for going the Apple route, even if it means having to buy your way into it. (Presumably, subsequent repairs will be covered by guarantees on the previous repair.) The exchanges are, I understand, current models. For obvious reasons (17" screen) I would not like to exchange mine. With 16 GB RAM and a 2 TB SSD mine still knocks the socks off the new 20" iMac. You might feel otherwise about yours.
Good luck!