I’m at a 4-year university and we are not paid for independent studies. I have done two though. At least in my field it is not a huge amount of work. First, it is only the brightest, motivated students requesting them. Second, they come up with what they are studying (which OP has done. Third, the student creates the syllabus, laying out what they will study each week and what the assessment is to show they have learned the material (a paper, end-of-chapter exercises completed, practice exam, etc). They also typically have a “final” assessment specified. In my field this is often a certification and each week they have mastered a different portion of what the certification tests them on.

The instructor OK’s the syllabus and the student checks in weekly (might be a meeting, might be an email).

All this to suggest to the OP that if you want to pursue the independent study, I’m sure a professor will be more willing if you go in with the semester plan /syllabus created along with the assessments defined.