As a followup, I have a Role setup called Scholarships. Here are screenshots of what the Role can do: https://www.screencast.com/t/Cb4NEOLk and https://www.screencast.com/t/lrlZz8uL6Xf and https://www.screencast.com/t/13cjfAilwgE8 and “Force Custom Post Types to use their own capabilities” is still enabled.
