If you could please elaborate on the why SSDT will fall apart? The database design is handled by 2 devs while the other dev's use the stored procs.
Because SSDT relies on you having access to the production system to do checks against, and write the "upgrade" scripts. This is fine in a mom and pop shop when you have one box and two devs, but if you have many servers and many devs it just isn't sustainable.
In the real world, a developer does not have access to a production box unless they are needed to troubleshoot something.
It might seem a bit overkill, but it is always better to try and get a solid development platform going no matter how small the systems you are working on. If/When you ever apply for another job, I'd be much more impressed with someone who might not know MSDN Books Online definitions off by heart, but was able to put basic source control and other things in place in a smaller operation.