The btrfs-convert tool hypothetically leaves the ext filesystem all but untouched, and COW's the needed filesystem metadata onto the end of it, with data modifications coming thereafter (or intelligently stored within the free space of the ext system). You wait until you feel comfortable with BTRFS, then delete the preserved ext system and run a balance, which rewrites all data to disk in the usual structure. Alternatively, the preserved system can be restored, although I don't actually see instructions for that.
https://btrfs.wiki.kernel.org/index.php/Conversion_from_Ext3
I love btrfs and would trust it but am glad to have backups of irreplaceable data.