TL;DR:
You're better off learning how to plan your time and working on your networking skills.
I'm from the UK so I had to go and look up what a Chevy Silverado Single Cab actually was.
Having seen photos I think there's likely to be no chance of setting up what you're asking for: Sound proofing a Chevy Silverado isn't likely to leave you enough room to sit in the cab without scraping your head, and your only other option is to build onto the flatbed - Do you have the money (it WILL cost a LOT), the skills (carpentry for a moving vehicle is NOT the same as carpentry for solid foundations) or the time (there are no off-the-shelf options here) to do that while preparing yourself for your school? That's unlikely for almost all of us.
My advice would be to get yourself a strong portable set up (laptop, small keyboard controller, decent headphones, whatever plugins and sound libraries you need for your style) and work with midi/samples to build your tracks as sketches while you're on the move. You could also use this setup to build rough mixes. Then you'll only need the campus studios to record a few sessions (vocals/instruments), finalise the mix, and master the completed track.
This means that you won't need as much time as the students who are doing all the structural work in the campus studios and you can fit into some of the smaller gaps that they leave.
One of the things they're likely to teach you is how important it is to plan a session. A well planned session can be completed so much more quickly and effectively than just turning up to the studio and winging it. If you're working on your tracks in the car/dorm/7-11 parking lot/wherever then you'll naturally need less time because your tracks will already have structure and you'll have a stronger idea of what you need to accomplish in the campus studio. Going into a studio, you'll know exactly what you want to achieve will save you lots of time and headaches (not to mention saving money in the once you have to pay for studio time).
I suspect that studio time at the school will not be allocated on a first-come-first-served basis. It's more likely that you will be assigned (in teams to begin with) specific time in studios with specific setups for your assignments. Use those opportunities to make friends with the teaching staff and technicians because they are the ones you'll want to talk to if you want to stay in the studio after hours.
Also, learn which of your fellow students are best at which jobs - You can call on the best ones to help run your sessions faster and more effectively too! That one guy who really knows his way around a desk, the girl how really understands mic placement, the kid who's just always happy to be there and will happily run and get things for you... Other people will also be looking at you for some of these qualities - strike up some mutually beneficial relationships with your fellow students - they may well last beyond the school and lead to business relationships later on.
Finally, whenever you're in the studio, be professional, be courteous to the staff, and leave the place clean and tidy even if it wasn't when you got there. Your future bookings are far more likely to be accepted than someone who treats the place badly - You're also more like to be invited to take part in other 'special' sessions with external artists/producers that the school might organise every now and then.
