Hi Jason Rice,
By design there should be no real difference between a space and subspace, outside of a sub-space having a specific "parent space" As such, if you are not seeing the option to create a project within a specific space, the project content type might not be enabled. To check this, as an admin, you should have access to the manage >> settings page for the space.
However, if projects are enabled within the space and you are still not seeing the option to create a project, please submit a case in your customer group ( MyJive Secret Support Group Administration FAQ ) as a next step where a member of our support team can investigate further into your specific instance.
Thanks for your response! After reviewing the parent spaces again and looking at the activity page settings, I then saw that "Projects" was not checked to be an included type.
Thanks for your help!