Dumb question:
If the boards you are gluing together are single sided boards don't you end up with either a double sided board OR a single sided board with a layer of copper in the middle (depending on which way you glue the boards together). If you end up with a layer of copper in the middle your leads going through the board are going to short out on the center copper layer. If you create a double sided board then that would not be true to the original - would it? Maybe I missed something. Either way gluing two boards together isn't going to look like the original. It seems you went to a lot of trouble to find the original board material all for not.