Do you mean that if they can't replicate my issue after I drop off my laptop they will just give it back to me and say, "Sorry, nothing wrong with it"? as it sounds like you're saying they will try to replicate the problem and if they can't, they won't acknowledge that there is a problem.
Yup. Why would they replace seemingly perfectly good parts for no reason? Any repair place would and should operate under the same general guidelines -- while they may have a ton of money because they're a big corporation, it still makes no sense to replace parts that, under testing, seem to be operating normally.
You can instruct the person who takes your laptop that the issue occurs sporadically, and your computer may need to be powered on for quite a while before the problem appears. The techs can then try and replicate as many factors as possible that occur with you when the problem appears -- it's not like they're going to boot it up, see the login screen, shut it, and say, "Done! Looks fine to me!"
If you truly have this problem (and no one here doubts that you do, but someone else has to see it actually happen [preferably a tech] in order to fix it), then Apple techs will see it and fix it.
Hell, I can't get it to produce the dark lines I described every time I boot it. Some days it does it, other days it doesn't. For example, it didn't produce the lines when I started it a few minutes ago.
I would suggest explaining this verbatim to the person writing out the tech ticket. Pictures or a video of the actual problem would seal the deal.
There are several online articles stating that Apple has acknowledged an issue with the the NVIDIA cards in exactly this model of MBP. I was hoping that this would have been more than enough to get this sorted out without a lot of fuss.
Also mention this. Bring documentation (printout of Apple's website page acknowledging the NVidia problems). Don't assume the tech knows every single recall, problem report, or hardware fault that Apple's owned up to. Most don't.
As a Mac man, is there anything you can suggest that I can do to make sure this is dealt with correctly and that I either get the graphics card replaced (can you do that with these?) or that I get a new, replacement laptop of the same spec, but without the defective graphics card?
Apple has the power, and they wield it quite a bit if you're persistent and polite (but persistent!), to replace the entire computer if it's not feasible to fix. I assume that your laptop is still under warranty, and as such, you can visit any Apple store (be sure to call or make an appointment online, otherwise, during busy times, you WILL wait for quite a while), and they'll take care of everything for you. Visit an Apple store that you feel comfortable going back to in order to pick up the laptop when it's fixed -- don't expect Apple to ship it back to you or send it to another store for you to pick up. Drop it off where you want to pick it up. Bring documentation, receipts, proof of problem, warranty info -- act like you're preparing for court and going on trial to defend the fact that your MBP has a problem. Don't expect Apple to do the research for you -- do the research yourself, get your documentation and papers and receipts in order, and explain everything to the tech in a straightforward and organized fashion.
Other than that, I think it will be a smooth process. If, in fact, it's hardware related, and if, in fact, it's still under warranty, then it should be as simple as taking the laptop in to the Apple store at your pre-approved appointment time, handing it over, then coming back to the store for pick-up when they call you.
And be sure to back up anything you want to keep before dropping it off.