Assigning Categories to products in WooCommerce when you LOTS of them

I have a client that has a WooCommerce site with 287 product categories. The category selection process is very time consuming and not user friendly as the category selection box when you are editing an item is so small. I have installed a category search plugin (Admin category search pro by Atilla Ordog) but the search is not very useful because many of the categories are nested and require you type in the ascii right arrow symbol to search for child categories. He is finding that using Ctrl-F and using the browser search is more efficient.

My client would much rather have the categories appear in a separate window (possibly a lightbox) where he could see the full line of the category and navigate through them quicker. Do you have any suggestions (code edits or plugins) that would make selecting categories easier when you have LOTS of them?

The site is