At the risk of being too blunt, a key thing that makes a difference in graduate school recommendations is how they value the judgment and assessment of the recommender. We can all whine and complain about how unfair this may be, but, pragmatically, it matters. They are trying to figure out how you will stack up with the students (faculty) at their university. A recommendation from someone who knows the caliber of students at their university (and whose assessment they feel they can trust) is much more meaningful to them (and carries more weight) than a recommendation from someone who doesn't. I'd suspect that this "prestige" of the recommender (on a good recommendation, of course) carries more weight than the "prestige" of your degree.
And, I'd take that into account when considering internships/coops. If you're going on in academia, working with (and impressing) someone whose opinion the academics will value can be a net asset. Who are they going to value? -- again, practitioners who will have known the caliber of students they are looking for (so often from the "elite" schools they respect, if you will).
One phenomena which you should be aware of is the "spreading" of faculty. The big universities produce most of the PhD's, but only employ a small fraction. Consequently, Prof's with backgrounds from the top schools end up everywhere. In this sense, the variation among students and student culture among schools can be larger than the variation in faculty talent.
What you miss at a "lesser ranked" (or teaching/non-doctoral) school is uniform faculty quality, uniform student quality, the strong cultural value of excellence, and facilities. But with work, you can find the excellent faculty members, the best students, and get a great experience out of it. Talk to the experts in your fields about who to look for at these universities (esp. use LSMSA alums who may be experts or practitioners in the field to act as experts or help you identify experts).
Returning to the recommendation issue above. If you can work with someone at your university who is known and respected by faculty at the more prestigious schools to which you may wish to apply for graduate school, their recommendation will be meaningful, reducing the problems I detailed above.
While you were chosen for LSMSA as the best-and-brightest of Louisiana, for college admissions you are competing against the best-and-brightest nationally and internationally. That puts you up against students from other math and science schools, from some excellent normal high schools, and from dedicated, private college preparatory schools. My experience upon arriving at MIT was not that I was ahead of my peers, but rather that my LSMSA education brought me up to equal starting terms with my peers from around the world. I have been surprised at what is covered in some of the "normal" public high schools outside of Louisiana. Coming straight from normal Ouachita parish public schools, I would have arrived at MIT with a sorely deficient background, and more likely, would not have been seriously considered as an applicant.
The benefit of going to LSMSA is not that you get to take college-level courses, but that you get a high-school curriculum on par with the best high schools in the nation so that you are ready to attend the best universities in the nation.
I have now seen many examples of students who aren't really ready for college, and who are doing everyone (themselves, their parents, their university) a disservice in going through the motions. Often it's just a case of maturity---they should really wait and come back when they are older and more ready to learn. The same people 2--4 years later will be excellent students.
I count my brother as one of them. The first time through college, he wanted to play around. He didn't have anything that excited him or he was passionate to learn about. He got bad grades and exited with an associated degree. Then he worked for a while doing technical drafting. He found something he liked, and he found that he didn't have the knowledge and skills he needed to be anything other than someone else's draftsman...and these guys weren't smarter than him, they just knew some stuff he did not. The second time through college, he had a mission. He had something he wanted to learn. This time it was fun. The courses were all good stuff (even the math!) that he had a use for. ...and, when you want to learn the stuff, the grades are secondary (but tend to fall into place). He now has a Master's in Architecture and has found a life calling which he enjoys.
For another (excellent) description of this phenomena, see Phaedrus' demonstrator in chapter 16 of Zen and the Art of Motorcycle Maintenance (Robert Pirsg).
Unfortunately, our university system is setup largely to review and accept students right out of high school. I'm sure older students who have taken some time off after high school will have some different challenges with the college admissions process.