I think it's clearer now, and I think you're right to wonder whence originates the stack overflow message. My guess is that it is the browser. Over the past few days, when I have had many dialogs come up in the debugging process, I got used to seeing a stack overflow message, and I just automatically assumed that was because the instance of IE7 could not handle all those dialogs (almost certainly, given our environment, due to lack of RAM).
Now, I have just put everything on to a MOSS virtual machine that runs under sufficient RAM (and, admittedly, with IE8), and have run the same code against the same data samples, and there was no error message.
So, let's presume--until proven wrong--that the error is due to limitations of the browser.
By the way, also putting this application on SP2010 showed clearly that another of the SPServices instances needs async:false. So, that makes three. The rest did not generate any problems with the default value.
Your instincts have prevailed, and the browser appears to be the culprit here.
Thanks for the help...
Michael