Hi Duke,
Most of what you want can be done via the API, although maybe not exactly as you envisioned. A few key techniques are interesting for you
* Embedded App SDK: With the embedded App SDK you can create pages and popups _inside_ the admin to append to the administrative experience of the merchant or user. I don't think you can actually do it in a panel underneath an existing page, but you can generate a link to your app's special page for this. On this special page you can then do all the sorting etc.
* Metafields: With metafields you can add custom properties to certain objects, like collections. These metafields can then be used in themes or retrieved by your app. In your case you could save the URLs to the images of the collection to be consumed by your rotator. For using metafields in templates see: http://docs.shopify.com/themes/liquid-variables/metafield
I hope this is the information you were looking for.
Maarten