It was cold and raining, and took a long time. But it was well worth it.
Here is the mount I came up with to hold Explorer 1 up at a 45 degree angle:
The main piece of white plastic is simply a section of 6 inch PVC pipe coupler, cut down to the shape needed. Note the holes for mounting screws to the body.
A few weeks later, the display is still standing, despite wind and weather. So far, so good!