You wait 3 days and ship 15000 on a single livestock carrier. The trip will take a while but will be "cheap" and efficient.
For example Italy had about 126k immigrants last year so one big ship every month could have solved the issue.
For immigrants who refuse to provide documentation/identificatiin you can just dump them on an isle like Australia is doing. After all nobody is forcing them to conceal their identity. I'm pretty sure that after a while less and less people will be willing to spend their money and resources knowing they will be deported back. At least the economic immigrants.
The less are deported the more will come.