Jose, I've found a partial solution.
I couldn't find the files via FTP because they are located in the WordPress Database, not in the installation files. I'm guessing a simple DB backup is all you need to keep your sidebars but if you're like me, you'll want to keep the individual files in case you decide to flush out the DB and start over.
Here's a little rundown on locating the sidebars for anyone who's interested. I'm a novice at this, so I apologize if my instructions are very basic.
- Log in to phpMyAdmin and select your WordPress database from the column on the left.
- At the top of the resulting page, click "Search"
- Search: "widget_"
Find: At least one of the words
- Search results appear above the search box; click "Browse"
- You'll see a list of entries. most of them are widget configurations.
- Among them you'll see "cs_sidebars". Bingo.
- If you customized any widgets (like placing code in the "Text" widget), you'll want to back those up too.
- Tick the checkboxes, and click the export icon at the bottom of the page.
- Select compression method (I chose none) and save to your comp.
From here you're on your own. If you click the pencil icon next to any of the database entries, you can view their contents. I checked out cs_sidebars, and it's beyond my understanding. I don't know whether or not any values in cs_sidebars will need to be changed if I reset the DB and restore cs_sidebars, so I'm just leaving it alone for now.
Most of my widgets are text/custom code, so I saved widget_text and will probably re-create my sidebars manually.
Unless.. Someone else can drop some knowledge on the subject