Diogo, thanks for your answer.
Just so I do this the best way, I'm trying to figure out how to do this using your suggestion of child pages. Is Ryan's solution in this thread what you're talking about?
With my limited knowledge, I think I can create a new template for the fields I want to be repeatable, but I'm not sure what code to use in my 'projects' template to allow repeatable instances of my new template.
Does that make sense?
Aaron