I have a forum running 3.0.7-PL1 premod.

All is working fine but I'm about to move to a new hosting company. But when I look in the ACP under the PHPBB SEO tab, the control panel for mod-rewrite and generating the .htaccess has disappeared!

Only the GYM sitemaps and RSS control panel is there.

Is it safe to reinstall the ACP module on the live board without messing everything up? If so, how do I do it?

Usually it's fine to do a reinstall. Just make sure you have backups. I've messed up a lot of times but always managed to fix bugs by starting all over again. Same goes for the database.