InDesign has a built-in TOC function. It is based on Paragraph Styles, so you would need a style that is used only for the items that will go into your contents.
It will work across files if you add all the files to an InDesign book.
The standard TOC requires intervention to update (Layout > Update TOC...). If you build it manually using cross-references it will update automatically as you work. The downside is that's more work to set up, and x-refs are known to be unstable across multiple files in a Book.
You can use cross-references to manually build a TOC that auto-updates.
(I don't know why you are opposed to using InDesign's Table of Contents tool, and clicking on Layout -> Update Table of Contents after making changes, but if you need need your TOC to update automatically whenever content is moved, then xrefs are the way to do it.)
Thanks for the responses, guys!
I'd used the ToC function before, but didn't know it would update if I told it to. I hadn't been using it because contents pages are always already included in the raw manuscripts when I set them, so I'd just been styling them, updating the numbers and moving on.
As much as I like this (admittedly new) job, the work comes at me fast enough that I don't always have time to experiment or research better ways of doing things since there's always something else to be working on (and throwing down a quick ToC is hardly the biggest time sink). So I appreciate the pointers. I'll have to give the ToC generator another chance, as well as play with X-Refs or that script at some point if I ever have the time.