BTRFS has been stable for years now as long as you don't use unsupported features like the aforementioned RAID5. A properly set up btrfs system is fine for production use, though note the "properly set up" bit, as a good number of distros still don't set it up right. I suspect the latter bit is why people continue to have issues with it (which is definitely a big downside compared to something like ZFS's "no admin intervention required" policy).

Regardless, in-place conversion is specifically a feature of btrfs due to how its designed. Since it doesn't require a lot of fixed metadata, you can convert a fs in-place by throwing the btrfs metadata into unallocated space and just point to the same blocks as the original fs. I think it even copies the original fs's metadata too, so you can mount the filesystem as either the original or btrfs for a while.