Are all your sites hosted on seperate account? Do you have cpanel control panel? If you do you can easily create backups of your site in cpanel and upload those to your new cpanel hosting account.
I haven’t heard of any problems with hosting casino information sites in the US. I think you would only have a problem if you were directly taking money for wagering. I know of a lot of bigger casino related sites hosted on US servers. You can get good shared hosting from hostgator.com or if you need dedicated servers from theplanet.com. Both their datacenters are in Texas.