I'm going to reply to this just to say that the attempt to upgrade to 10.9.4 couldn't possibly have gone worse. I will spare you the gory details but suffice it to say that I had to reinstall from scratch, which was made more difficult by the fact that somewhere along the line the failed upgrade managed to corrupt the thumb drive I used for installation. Fortunately I had a backup of that.
So I wound up having to do a full reinstall, but at least this time I used the newest Multibeast and saved the .mb file. But what was really my salvation was the OS X Migration Assistant, which is in the utilities directory (off of Applications) and also is offered after you do a fresh install. I had never used that before because I thought it was only for importing settings from other systems, but after watching a video I realized that it was good for restoring programs and data from a Time Machine backup, which fortunately I had (I was smart enough to keep that drive unplugged during the failed upgrade, so it didn't get corrupted). Basically it will restore everything EXCEPT the operating system (and any directories you have excluded from your Time Machine backup), and that is what you probably want. After using that and selecting everything it could restore, the system rebooted and when it came back up it looked and worked almost as it had before the upgrade. There were a few things that were a little off, mainly programs where the registration data had to be re-entered, but all in all I was back up and running in hours rather than days, as is usually the case when I do a full reinstall.
I probably would not have done that if this had been a major version upgrade, but since I was staying with Mavericks I figured it was worth a try, and am I glad I tried it. So if anyone else has a Hackintosh upgrade go south on you, try reinstalling the operating system as if you were doing a fresh install, then run the newest Multibeast, then immediately apply the upgrade (remember to fix permissions after each step), and then if that works use Migration Assistant to get your programs and data back from your Time Machine backup (check all the boxes to let it restore everything it possibly can). This will get you about 98% of the way back to where you were and most everything else is just a matter of letting software do its thing, or re-entering registrations (only had to do that on about three programs, but Little Snitch was one), or checking settings to see if they are how you want them. Basically it seemed as if programs stored their data in userspace (somewhere within my home directory) then I was good to go, but if they stored data someplace that's supposed to be reserved for the operating system then that was an issue, particularly for non-Apple software. That data is probably also still available in your Time Machine backup, but Migration Assistant won't bring it in because it doesn't overwrite anything that has to do with the operating system.