Okay, couple of things. First, AFLP (Amplified Fragment Length Polymorphism) is a polymerous chain reaction based tool used in genetics research. In simplified terms, it calculates the amount of sameness between your DNA and the DNA of anyone else, which indicates just Exactly how closely related you are and gives you an idea of the degree of risk for incest-related birth defects. Not all cousins are going to be in exactly the same place. On average, yes, there is a certain range where a cousin is expected to be relative to you. And under normal circumstances, you and your cousin being together is not going to be a problem vis a vis children and birth defects. But it does yield a situation where these hypothetical children are going to have more AFLP markers in common with Their cousins than you have with Your cousins, and the more this sort of thing happens, the amount of genetic variation between cousins becomes less and less. It can lead to a situation where, from a genetic marker standpoint, having kids by your cousin carries about the same risk as having kids by your half-sister. (A sibling with whom you share one parent, not two). So for one thing, there is a possibility that some of this has happened in your family tree that you don't necessarily know about. The genetic risk may be higher than you would initially estimate, you don't really know until you check it out. And for two things, this is a proposed course of action that probably (maybe?) doesn't pose grave risk to you or yours, but it does introduce an incremental risk factor to your family tree that may affect other people down the line. Sort of like how you might be affected by what your ancestors did.
The second thing is from a non-scientific, non-genetic perspective. Just from the standpoint of human relationships, is this someone who you sort of grew up with? I remember you saying you're 17, you're still a minor for goodness' sake, so it does seem like you grew up around each other as kids and as family members. Again, just from a relationship standpoint, it would be a different situation if you'd met her while getting your degree or after you'd gotten that good paying job, then you meet your cousin as an adult and things happen. But that's not your starting point. You did know each other as kids (don't know exactly how young, but as minors anyway) with your parents and her parents bringing you up, while knowing each other, with the expectation that you're family and you won't go on to pursue a relationship as if you weren't.
Regardless of what may have happened in early Islamic history- back when men could have easily been married by now, without worrying about school or the kind of job that you want. When some Muslim men could look forward to having up to four wives (why would you look forward to that?) When Muslim men could also look forward to owning slaves, and maybe killing some kaffir and taking their wives and daughters as sex slaves. (But treating them really well, of course, and we should always make a priority of seeing how well the slave owners were pleased with the situation). And yes, Muslim men would also sometimes marry their cousins. But even with that, yes Even with that, a cousin could be a mahram if the two of your grew up around each other as kids. That has always been a part of how mahrams are identified, at least this is what I've been led to believe and would someone please tell me if that's wrong and provide a source, maybe a fatwah that's really specific to this distinction.
The point is, some things change. You accept that you need to do a couple of things in order to support a family in your current situation. If you go back through Islamic history, you will find Muslim men who were married by your age, but their situation was different. You accept this. You accept that you can't own slaves now, sex slaves or otherwise. Going back through Islamic history, you will find plenty of Muslims who had both kinds of slaves. That doesn't mean you get to, because you really are in a different situation now. And congratulations, you found some examples of Muslims who married their cousins. Presumably after growing up independently, without being around each other as kids, and then meeting as adults and getting married. I assume. I'm pretty sure that's how it's supposed to work. You want to check on that? It's a worthwhile distinction to make. At any rate, this is something that's changed a bit as well, and maybe not even by all that much. I'm fairly certain that if you grew up around your cousin as a kid, both of you knowing you're family, that makes you mahram to each other. There is a social component to this. Of course I'm not a Muslim, but as far as I'm aware, the reluctance your parents have is quite understandable and not just from a modernist standpoint.