Dave as many have stated CA glue (aka Super Glue) is the only good option at this point. You have loose pieces because some of the plaque did not get glue applied to it when you did the glue up. Now let me suggest a better way to glue to prevent that from happening again. This is a trick I learn from Dirk Boelman many years ago. Get yourself one of those 1" painting trim rollers. The cheapie kind. They can be had at Lowes, Home Depot, your local hardware, and even Walmart. Also get a length of black foam pipe insulation. The diameter of which will fit over the wheel the paint roller sleeve is on. Replace the paint roller sleeve with a like length of the pipe insulation. Then when you need to do a glue up squirt some glue (any brand wood glue) on a piece of wax paper. Roll the foam applicator in the glue and then roll the glue onto the back of the piece. You want a nice even coat. Be generous but don't glob it on. Just like paining a wall with paint. After coating the back wait 2-3 minutes for it to start to tack up and them clamp your pieces together. After the glue sets nothing will come apart or be loose. The foam roller can be used 100's of times before replacing. You can clean it with a wet paper towel immediately after use or after a couple uses peel the dried glue from the roller. I prefer the latter method of cleaning.
Let me know if you want some pictures.