Well, I'm not quite sure that switching to github is a transparent solution, without having your own git server somewhere, because I don't think hosting 1000+ websites can be possible to host using a free solution.
Personally, in my own workflow, I have quite a few websites 100+ in production and almost all of them are bricks that other teams use through Dreamweaver. Therefore and to avoid keeping an infinite list of sites in the DW IDE, I only use.STE configuration files.
on a protected space I systematically store these configuration files there. changing the file paths within these files results in a replacement system operation, for my part (and you will certainly laugh) I use Director (from macromedia) to perform mass file manipulations in a very flexible way.
Anyway, this is the track I would use, so in short..... export all your sites as.STE. Change the paths in batch processing (Note PAD+++ must do this perfectly)... and reimport your STE with the new paths...