Currently there's no way to perform a site import into Confluence Cloud when using Confluence + JIRA due to its shared user base. However, importing space by space is not feasible in certain cases, specially when the instance is big.

It would be awesome to be able to import site even though we're using Confluence + JIRA or at least have an automatic way to import spaces in batch or have Confluence to manipulate the Site XML file to import the content accordingly.