There's no native way to allow a role to add/edit values in only some Custom Lists and not others, is there? The only permission that exists is for all custom lists globally, right?

No, AFAIK You can convert the Custom List to Custom Record and take advantage of the permissions

Custom record gives you more flexibilities - workflow, scripting, field sourcing etc.

Makes sense, but at the moment not worth for my company to convert it to a custom record and refactor scripts that use it just to let that one role have higher permissions for the one list.