Quick Update. Took my new iMac to the Apple Store and discussed the situation. They could not find anything wrong with the machine. They are very interested in the findings and suggested that I use my old Firewire Audio Interface to see if that worked. I had to pick up a Thunderbolt Firewire converter and pull up my house to find an electrical adapter for the Presonus, but I did what they told me to do. I also looked at the Presonus website and was disheartened when I saw Presonus stating on their web page that the Inspire GT would not work under Mavericks. They are wrong ! Although I had a little more noise when compared to the Focusrite, the Inspire actually worked well with none of the cackling sounds and I was able to work for about 4 hours. The cackling sound occurred once in the 4 hour period, but I attributed that to my overloading a distortion effect on a guitar. The bass was clean and I had no problems. One thing that was also interesting was the fact that I had no latency issues despite using a Firewire-Thunderbolt converter.
The experiment today showed, at least from this effort (N of 1 may not mean much), that it was not the entire board that is a problem, but more likely than not, faulty USB Audio drivers in Mavericks.
This may also address another issue that I have seen posted here and elsewhere, that that the USB Haswell problem continues on both platforms. I was able to use a Seagate 3 TB back up drive without incident this morning. At a speed of approximately 3 gb/minute I was able to back up my entire FD hard drive without a glitch. I am also using another to run Time Machine. There was a problem last year in Windows Land with the Ivy Bridge / USB 3 ports. From what I read, there was and possibly still continues to be a problem with the down conversion from USB3 to USB2 devices. The Seagate drive is a full USB3 machine. My Focusrite Audio Interface is USB2. I also noted an issue with an Andrea USB Headset (USB2). It is possible that the same USB3->USB2 down conversion issue is happening with the Haswell / USB3 combo also.
I am no expert on any of this, but the finding of my Thunderbolt interface working without a glitch, even on a down conversion from Firewire 400 to Thunderbolt is reassuring that I won't have to take back my machine permanently. I have no idea how the interaction with FD drives and the USB3 sound are related. But the fact that most of the complaints have been Haswell related recently, but also interspersed with complaints from people using earlier iMacs and Macbook Pros leads me to think that the relationship is mostly a USB driver issue.
My only hope is that someone from audio land give the folks at Seagate a call because they seem to be doing something incredibly well over there. Their 3 TB backup drive is compatible with Firewire 800, USB 3 and Thunderbolt. And to make things interesting, I have just read that Microsoft also solved the USB 3 problem with Windows 8. However, to be honest, I would not give up my Mac for a Windows 8 machine.
I am very happy for this forum and others. Without it, I probably wouldn't have conducted my own experiment this morning. I would also like to give a shout out to my local Apple store. They were very helpful.