You can still ask to be moved to another of their servers, that would be a matter of a few hours for them and it would require zero dot zero work on your end :)
Also, it's natural that all the sites behind the same machine (physical or virtual) share the same IP adress. (Also, it may be OK to share the same machine as thousands of domains, maybe 95% of them are simply inactive, there's no telling.) It's your host's job to direct requests to the sites after it arrives to their servers ;)