First, I prefer Karmel Shuttle over Super.
Renting a car at LAX involves a shuttle to the offsite location. This does take some time, but not a huge amount of time in our experience. And you have to factor it in on your way back, too. It's not more complicated, in my opinion, it's just a time thing.
Since you have a time change going on, will you be up to dealing with that at 2am...5am? for your brain and body? Might be a lot easier to just take the shuttle.
Assuming you've priced out exactly where you would rent locally, and it's truly only $80, the shuttle and the local rental sounds better. Where are you renting from and staying?
The other issue, and I speak from experience here, is that when you pick up a car at night, it's HARD to inspect it. So if you're not taking the extra insurance (oh, make sure your car insurance covers a rental car...but the extra insurance covers the time that car is out of use, if they have to fix it, and NO car insurance I know of covers THAT), you'll want to inspect it on pickup. I picked up after midnight...dark car in a dark-ish parking lot, and 2 months later Alamo tried to tell me I had damaged the car. Well, since it literally could not be inspected, and it had been 2 months, they couldn't prove it was me and they dropped it after another 2 months...but that was a very stressful time for me. So either make it so you can inspect the car at pickup and dropoff so you know the condition of the car, OR take that extra insurance. (advice given because you state you have no experience in car rentals)
