I've done a fair bit of re-formatting myself, and I feel your pain. I had to copy and paste from PDF files, so it was probably even worse than starting with Microsoft Word files. Here are some suggestions on how to speed things up.
- Rather than going through the document in a linear way and applying the various different formats as you meet them, go through it multiple times, each time applying a different format: first mark up all the headings, then the bullet lists, then numbered lists, tables, etc.
- Learn all the keyboard shortcuts you can, avoid using the mouse.
- You can select a whole set of list items and format them in one step.
- Theoretically, you could try using Search and Replace to find bullet list paragraphs by their default formatting, and replace them with the named style "List Bullet", but I found this difficult to achieve.
- Set Draft view and turn on the Navigation pane, and turn on the Style Area window so that you can see all the paragraph style names as you are applying the formatting (see screenshot below).