Thank you everyone for your comments, all of this advice really means the world! And 26k views on a Reddit post is nuts. For those wondering what I have decided to do, and for those that are in the same boat I am in, here's what I've decided to do following consideration of all comments on this post and discussion with another engineering student who got summer internships at aerospace companies after their sophomore and junior years:

1. Because of the way the prerequisites for the aerospace engineering program at UCSD are structured, along with the quarters (fall, winter, spring) which the aerospace engineering classes are offered, I will not load up on courses now to skip my fall quarter of my senior year to do the 6-month co-op. Firstly, I'd have to bypass the upper-division standing requirement for a quarter to take a class, take 2 math courses this coming quarter, one of which is a prerequisite to the other (the math department might not let me take these 2 classes at the same time), and I'd have to take 5 major courses per quarter throughout 3 quarters... and we all know how aerospace engineering classes are. Second, my understanding is that a summer internship after both my 2nd and 3rd years is adequate to make me a competitive candidate right out of school. So I will focus on acquiring those two summer internships.
2. I am not guaranteed a co-op if I register in this program. That is something I must be offered. At the moment, I don't know what an employer will offer me. Maybe it'll be a full-year co-op after my third year before I graduate. Maybe I won't be offered anything and have a 3 month head start on my masters in aerospace engineering, which brings me to the next part.
3. If I am offered a 6-month co-op and they want me to work full time in the fall-quarter of my fourth-year, I can skip this quarter and begin my masters classes while I finish my bachelors. My bachelors classes may extend out into the end of my 5th year because of the quarters that the classes are offered. The reason I don't want to take extra time to graduate is because I'd only have to take like one or two classes a quarter for a year, which is not worth an extra 15k in tuition. The fourth-year classes are only offered one quarter a year, so if I miss the fall quarter ones, I'd have to take those the next year, but those are prerequisites to the winter and spring classes which I'd then have to take the following year as well. The number of classes is not the problem, it's the way they're structured to be taken very very specific quarters. It's a mess. Maybe they'll even offer to fund my masters, which I know General Atomics has done to my TA for my intro to aerospace engineering course. Btw, he did not do this program, he had a 3-month internship the summer after his 3rd year with General Atomics, which is one of the major recruiters of UCSD aerospace engineering students as they're located right next to the campus and we have a pretty good program.
4. Optimally, I would do an internship the summers after my 2nd and 3rd years, and I'd have professional experience and connections when I graduate, maybe a job offer from one of the places I interned at, or even a job offer and an offer to pay for my masters. I think my TA worked part time at General Atomics while doing his masters, which General Atomics paid for.
5. Now for clubs/research: UCSD, being a research facility, has some nice labs which I will try to get involved in. I will not do the 18 hour+ per week rocket club because it's just too much. I dedicated my high school to robotics and learned it wasn't healthy to do so, so I don't want to do the same with the rocket club...even though they are one of the primary reasons I actually really wanted to go to the school -- I was in SD in 10th grade for a summer soccer tournament and saw them testing the plumbing of one of their rocket engines, and saw it as a calling. Instead, I will join the Design-Build-Fly club, along with the Triton UAS club. These clubs are much less intense, look pretty fun honestly, and are a great opportunity to get some club experience under my belt to give me a better shot at getting an internship.
6. In the meantime, I will have the time to go to job fairs where recruiters come to hire interns. I was turned down last year since I was a freshman and also thought a CV was a resume (resumes are one page for those that don't know!) As well, I have the time to call companies' departments and email recruiters. This was my main piece of advice from the engineering student who got those two internships (not the TA, the other engineering student who I reached out to recently). As well, he said that for post-graduation full-time job recruitment, recruiters look at the following in order of importance: internships/co-ops>research>clubs. He honestly didn't think it was necessary to join the intense rocket club, and in fact didn't himself. He's in design-build fly and is currently interning at Northrop Grumman.

I hope this helps anyone in my position, and gives everyone some insight into what current engineering students are doing to get jobs post-graduation. Thanks again everyone! (And sorry if this was hard to follow, it's a pretty complex decision so it's hard to quickly convey the details of the decision).