I discovered yesterday that the problem I described in the original post is avoided anytime the document template you are using is a regular document type. In my case, I was using an Excel template rather than an empty Excel document (formatted of course). So it was just a matter of doing a SaveAs in the open template and saving it as a workbook, then replacing the .XLT file being used by the content type I define with its .XLS mate.
I realized that the document type of the “template” was forcing the SaveAs functionality to shift from the default of XLS to XLT because that was actually the file being used.
The key insight that I was forgetting, is that files are opened from SharePoint as-is; SharePoint is blind to Office document templates.
I guess it really is better that MS has decided to drop the Office moniker from SharePoint 2010. Unless MS truly integrated SharePoint with Office, they were no better off than any other document collaboration/management system where Office documents are concerned.