Thanks for the advice!
When I say "redo the site's look and feel", I mean changing basically everything except the posts and comments and some of the pages on the current site.
Ok...here's what I have decided to try.
Make the test domain, copy the existing site there, make my changes and prep it to migrate to the live site.
I'll put the live site in maintenance mode, and do a complete backup and save that somewhere safely off the live site.
Before migrating, go to the Admin menu, Tools>Export, select All Content and do an export.
It says "All content This will contain all of your posts, pages, comments, custom fields, terms, navigation menus and custom posts." I hope that means that it also keeps attachments, images etc.
I'll use BackupBuddy to migrate the test site to the live site. Then, I'll import my exported data into the live site and disable maintenance mode.
If all goes as planned, this should do the trick.
I''ll let you know.
My only concern is that I will be creating content while creating the new look (for sliders, landing page, and so on). For example, if I create a cool new Home page, it may be overwritten in the import of the old data (since I had an old Home page in the old site).
WordPress says (http://codex.wordpress.org/Importing_Content#WordPress) "WordPress will then import each of the posts, comments, and categories contained in this file into your blog", but the exporter also mentions pages, custom fields, terms, navigation menus and custom posts as a part of what is exported - so I am not sure what will happen.
Well....I might as well dive in. As long as I have backups, I should at least be able to get back to square one if the whole thing craps out on me.