Using FileMerge to compare (Mac OS X graphical diff), no differences between the page.tpl.php in the scf_base theme and the page.tpl.php I have in scf.module.
But the site doesn't look the same at all. That means the reason moving template files to the theme layer failed is because I am not calling them right.
Had to put them in hook_theme_registry, of course.
Once that was done, progress began in earnest. Breaking the site, of course.