Is there reliable way to migrate the project to a Jira Cloud instance, which has already other existing projects?
There is no FogBugz migration tool for Jira Cloud.
There is an option to migrate to Jira Server, backup it and restore on Jira Cloud, but it will erase all data. I migrated the project to Jira Server, restored it on the test instance of Jira Cloud, but I cannot find a way to move this one project to destination Jira Cloud instance.
There is an option to restore a project from backup (with some manual work) but only restore it on Jira Server (if I understood correct).
Plugins "Project Configurator", "Configuration Manager", "J2J Issue Sync" are available for Jira Server (if I understood correct).