@reynlds
I believe (with some evidence from the Dev Console) that the way that Edit Sections actually works is that it's calling an enrollment on the section and then (if needed) unenrolling from the deleted sections.
Are you potentially calling the Enrollment endpoint on the course ID instead of the section? If so, maybe switching to the section ID endpoint (like the one I linked above) will maybe work?
Here's what I did in the beta instance to see what endpoints Canvas was hitting:
1) Enrolled myself into a course, accepted invite, put myself in a section (Section 1) and created a new section (Section 2)
2) Go to the People page -> Edit Sections -> deleted section 1 and added myself to section 2, click update.
Here are the calls that I'm seeing in the Dev Console - It'll call the enrollment endpoint first, then unenroll (to ensure that you stay within the course properly).
Does this help?
Edit: somehow I'm having issues with inline images, for some reason? I'll attach the pictures with the calls.