The project is looking very interesting indeed.
Jumping from graduate school to such an unknown and uncertain endeavor, dangerous and exciting no doubt. I wish you all the luck in the world.
While I do understand the risk associated with forking, I do believe quite strongly that source availability is paramount. While I have no doubt in the good faith of the developers and any security auditing company involved, it would add a layer of uncertainty that could lead to unpleasant situations.
The code does not necessarily have to be FOSS, meaning that the licence with which you decide to release the code could perhaps be clear on its stance regarding derivative work, but the full source code associated with the entire system should be available to the whole community.
This brings up a really interesting point. There is no doubt that this project will be FOSS. The only question is when. Without contributors who fund the developer to build and innovate, there can be no project. However, by not making it FOSS the project would do the larger world a great disservice.
So on the one hand we have the desire and need to make it FOSS, and on the other hand we have an ethical obligation to the contributors to protect what they essentially built - in order to ensure their contributions weren't in vein. Even though the larger world benefits from the created knowledge, we can't have a situation where those who contributed become martyrs. That would kill the model in the long term. This is a question Ethereum is also thinking about.
I think there are two ways that can run in parallel that we can use to deal with this question:
(1) Make everything FOSS so everyone can benefit from the knowledge but keep one component out that is not straightforward and critical to the functioning of the cryptocurrency system (something PoS related)
(2) Wait for the community to grow sufficiently large so that the network matures to a point where there is no incentive to migrate overnight to an identical clone with nothing novel (this may be more of an unsubstantiated fear than a real possibility, however)
That's my take. Forgive me if my logic is flawed. I'd love to hear what you think because this is something that remains untested for the most part.