You can use the upgrade tool which is even easier if you are on a current version of owncloud. Even though the article doesn't say anything about updating from owncloud, the first article I posted does say you can use this method on current owncloud servers. You just switch the update channel and search for updates.
Now log into your new FreePBX system and it will show the Apply Config warning.
At this point you can go through the new system one piece at a time and make sure you are good.
Change a couple extensions to point to your new PBX and make sure they register and can call each other.
Once you are sure that the basics are working, disable the trunks on the old system, enable on the new system, and verify outside connectivity works.
Finally, you can change the rest of the extensions.