Truly BIG Blue.

I ran into the same situation when I was a practicing engineer. Before I/we signed the contract I just added a phrase to confine the scope of the agreement to any work developed during my employment and related to the scope of my engineering activities on this project. and had the HR manager and I both sign it. Legal details notwithstanding, I assumed that would sufficiently muddy the waters to keep them from going after anything I developed that they were not paying for.