I've got a server happily running Fedora 19, but am thinking about living in a calmer, more stable, less bleeding-edge world and moving to CentOS 6. Is it possible to make this move in a straightforward way -- just sorta run the CentOS installer over the Fedora installation, tweak a package here and there, and come away running CentOS? Or is this a hairy, unreasonable thing to even think about doing, and that starting over with a clean disk is, in the long term, faster and easier? Thanks!
You're talking about downgrading virtually everything on the system. Not to mention the slight incompatibilities throughout the system, starting with systemd and going onward. There is no reasonable way to "install" CentOS over Fedora 19. You're going to have to do a clean installation.
Don't do that.
It is indeed a hairy, unreasonable thing going from Fedora 19 to CentOS 6 like you describe, I doubt if it's even doable. RHEL6 was released 2009, and is derived from an older Fedora version than 19 is, so even if it were possible what you are suggesting, you'd be looking at downgrading every single package, not to mention systemd etc which makes Fedora 19 a very different OS from CentOS 6.
You'll save yourself a lot of headache making a clean CentOS 6 installation, and then migrating your deployed Fedora 19 stuff onto there.
I would setup identical (or even upgraded) hardware along side it and move the services over one by one. But I live in the world of non-stop production environments.
Can you run the CentOS installer over the Fedora installation? Yes. Is it recommended? No. It's not supported and you might end up needing to wipe the disk to get it working properly in the end. For the best result, wipe the disk and start over. Either over your existing or on a new server next to it. In either case, make sure you have a good backup before starting.