RE: Which Glue
White glue and a hair dryer. Just kidding. 30 minute epoxy is good but I have a short attention span so I almost always go with 5 minute epoxy.
Are you saying the vertical is glued right to the top of the horizontal with only 1/4-round to support it. If that's the case it's going to come off no matter how you glue it. You can add a couple vertical dowles from the stab into holes you drill into the horizinal/fuse. I need the guy that always draws the great images to help me with a diagram for this one.
Mike