Of course, before doing anything with your thousands of files, you made and stored a complete backup of the files!
If the template reference you need to change is in the 'locked' area of the child pages that were made with the template, can't you open the template and change it there? I suppose not.
You mention that the Template filename extension was changed to .dwt (the Dreamweaver extension for Templates); do templates in GoLive have the .html extension?
Try doing Modify > Templates > Open Attached Template from one of those pages and see which file it opens.
With luck, someone with this kind of experience will chime in.
Yes, I can change things in the template. The problem is in the "child" pages, where (at the very beginning of the code, before the "head" section) it has the left-over line " <!-- #BeginTemplate "../../bikeraceinfo2.data/Templates/bri-template.html" --> ", which references the old GL template location, while it now needs to read (in every one of those pages) " <!-- InstanceBegin template="/Templates/bri-template.dwt" " (I got that by just creating a new page from the template placed where DW wants it). And that line of code appears to be in a locked section in all child pages, won't let me edit it.
The Modify > Templates > open attached template is looking for the original GL template (per that code above), but that folder is no longer in the site, so it can't open anything.
If you have not changed anything else on the template, rename the template to the original name and recreate the original files/template structure. As you say, it's just not finding it with the template's altered filename and structure.
Tried that---the problem is, DW will seemingly only recognize templates when they are in the folder where DW wants them. "New page from template", "New page --> apply template", etc., all give you a list ONLY from the DW "Templates" folder, and I don't see a way to navigate to some other folder. Also, I don't think DW will recognize as a template a file named .html (I tried putting one of those in DW's preferred folder, and it did not show up on the list for "new page from template").
I'm afraid I'm getting closer to manually changing every page...