Admin with Less Access – Only Clear & Export

The plugin already creates the Sign Up Sheet Manager role…
Have you read the documentation?
https://stephensherrardplugins.com/docs/pta-volunteer-sign-up-sheets-documentation/

Another copy and paste from the documentation for you:

User Roles – Sign-up Sheet Manager

This plugin adds a new user role to the WordPress system called “Sign-up Sheet Manager”. This role is the same as the “Author” role, except that it adds the “manage_signup_sheets” capability. If you have users who you want to allow to create, edit, and view sign-up sheets on the admin side, but don’t want them to have full admin access, you can either assign them to the Sign-up Sheet Manager role, or use some type of role/capability editor (such as Role Scoper) to assign the manage_signup_sheets capability to them.