Didn't I just see a commercial product that works in a similar in fashion? I would stay away from wood glue, and I would advise you to leave the glue for 8-10 hours, to make sure that it was fully dry. You might want to leave some distilled water on the record after removing your glue disc to see [by touch or even taste] if there was any glue residue left behind. Also, if the glue doesn't come off easily, and in one big "glue LP", I wouldn't feel too good abut the process.
You might be onto something!