we had similar scenario. As Brenden Kehren said upgrade to version 8, just that you can use Staging. Then you can select what documents to stage no new instance.
Other options is again just to upgrade and then export (using export tool) part by part and import to new site. Similar to staging.
Final option would be (I had a chat few years ago with Kentico) to export content, unzip, change XML to fit Kentico 8 and then import them. Didn't try this, but it can be done.
We have used first option, it was easier.