I've been able to do this both for a .php migration along with a .shtml migration.
In the subdirectory, I just included a .htaccess file that states (for the .php case that you stated):
AddType application/x-httpd-php .html
This way, all files can still have the .html extension, yet are at the same time php parsed files.
I don't see how something like this can be a security problem, so I hope your hoster lets you add this little bit of .htaccess magic.