We already migrated the tables, but they are messed up. The styles are munged and the sidebars can't be udated and saved.
hmm. Both tables have the same structure (J! 1.5 and J! 1.0). The only difference is that on the J! 1.5 version you have a new table with categories and languages (_sidebar_languages and _sidebar_categ_manager).
So, first you will need to install the extension on your J! 1.5 and then replace _sidebar_styles and _sidebar_sidebars. Remember that on _sidebar_sidebars you will need to set all your items to General category.
Regarding CSS: by "backup", do you mean we should simply move the old /components/com_sidebars/css/xx.css into the new directory?
Yes.