In general, my usual approach of using global variables has failed. Some work, some don't. Various experiments suggest a problem with JavaScript closures, a subject with which I am too unfamiliar (but will spend the weekend on). Some confirmation of this comes from Doug Crockford, who notes that IE7 did not fix the IE memory leak that does in fact affect JavaScript closures in IE. Quite possibly, this is the reason I get the "Stack overflow on line 0" message (when that message moved to line 992, I got rid of it by removing one level of SPServices), which is annoying but causes no known problem. The same code and same sample data do not generate an error under later versions of IE.
My solution--workaround, really--is to use another SharePoint list as a temporary buffer. The actions against the contents of that list work while those same actions against a global variable array do not.