If your domain is already Geographically targeted ( .co.uk ) and you added Geographic targeting to another country, I do not believe you will see any difference in search visibility in that selected country.
Dave Elliott: If you use a country based TLD then i don't believe you can change the targeting!
RockandScroll Video SEO: Get a new host, one that has a server in the country you wish to target. Basically comes down to a reboot of your site. This does mean that all your rankings will drop and take time to go up if your site is properly optimized.