I've been using the standard Wordpress instructions to change my sites URL under a MidPhase business account. I found some of methods didn't work for me. Here's the approach that did work.
In the end, the Relocate Method worked well for me although I had to flush the cache or refresh the page to get it to display correctly.
However, after changing the two URL settings under the Settings > General admin page for my site, I still have issues with images on the site. In my posts, the href's for the images were still pointing at the old URL in addition to the TwentyEleven theme header images. There is a brief description about these issues in the WordPress article under Additional items of note.
I started using PHPMyAdmin to edit the wordpress database for my site and kept coming across references to the old URL in areas beyond just the table for my posts.
In the end, I decided it would be quicker to export my data using the WordPress XML export feature and create a new site with the MidPhase Softaculous.