Giving WordPress it’s own directory and using .htaccess Directory Index

This can be done. What you want in your .htaccess is something like

if directory do not exist in root
  change root to the wordpress directory

unfortunately I am not familiar with a way to do such a thing with .htaccess

The other option is to map each possible url directory to the wordress directory, but since url directories in wordpress are created dynamically when you add category, page, new post date and more, it will become hard to maintain the .htaccess. Maybe you will have better luck with special treatment to the current site URLs.

And this all assumes that you will not have conflicts in URLs between the old site and the wordress site.