Before you start formating and reinstalling, but after everything is backed up twice, I'd try to do an existing upgrade through Synaptic. If it fails, you still have the fall back option of preceding with a fresh install. If it works with no issues, you're a winner.
Now I have a few questions before I begin. I have my home partition separate from my root partition. Can I just leave /home intact an format only root? That could save me some time.
Everything I've read suggests you can leave /home intact and that's pretty much the only reason you really need home on a separate partition. I know folks that don't use a separate partition, ever. If I were you, I'd research everything I could to make sure I had my duck in a roll. Some but not all you would need to do:
Take note the user name and UID. On my install, with a single user, the UID is 1000. If you have multiple users, add them in the same order so the UIDs match. Also, when you're ready to install from the liveDVD, use the expert or custom or manual mode (forgot what they call it) so you only format and install the / partition.
You'll also need a list of all your installed apps and if I remember right there is a simple command you can run to get that. Either print it out or open Kwrite and copy and save it in one of your data backups.
If I cannot leave /home intact and must format both, then I will need to restore from my backup after the installation of 13. When I do that, it will also copy over all of the old dot-files -- will that create problems due to compatibility changes?
Shouldn't but if there are issues with apps in your current install, you'll be dragging all the old configuration files you got in /home to the new install with all the old issues.
If you use Kmail or Thunderbird, you may have issues if you try to save or backup your old messages. A topic I personally will avoid.
I have made several tweaks, such as editing the rtchibernate script in order to have my laptop suspend for two hours and then automatically hibernate to conserve battery. Is there any way o carry that over to 13, because I cannot remember exactly what I did

Also did something similar with my touch-pad.
Shame on you for not copying those scripts to Kwrite and saving them in your Documents folder for a rainy day.
Lastly, I have added some PPA's to my sources because I need the latest cinlerra and vlc to always be installed. Can I keep those, or will they need to be changed or updated on the new system?
Anything that happens in root, such as your source list, would need to be added again.
What I wrote above is not a guide but just some things to look out for. I personally never keep my old /home when I install or reinstall, so don't take what I wrote as gospel. Do your own research so you know the workings of your system.
What I do do is make multiple backups on different media of my docs, media files, fonts, photos, etc. Besides having all those files in my home folder, for me, that means creating a separate /data partition on the hard drive the OS is on, a /data partition on the second hard drive on the desktop, my laptop home folder and a separate /data partition there too. All synced with LuckyBackup (it's in the repos).
Good luck.