Final analysis
GP031029.mp4, which was 12:00 long wasn't used in the project and was deleted to reduce unnecessary file loading.
The Stabilized Fragment.AVI file is bad and was hanging VP - audio is many hours long yet the video is only about 4:36. It was replaced with a re-encoded version. Can't say what went wrong with the original deshaking of that file because...
The Stabilized Test Video 2.mp4 file is good. Both A and V are the same length. Stabilizing creates an AVI but this was an mp4. How was it done?
The Test Video Singling.mp4 was A/V UNlinked and being used only for audio but video was still a part of the load. Under the BIN Sequences tab Sequence 1 was right-clicked to create a new WAV using Save Sequence to a New Audio File. Singling.mp4 was deleted, which cleared the audio track, and the WAV file was added in its place.
Now the project contains two video files, one audio file and the VPJ control file. Export at 1080 is quick and the program no longer hangs.
In the future, suggest that you pare down the original file, retaining only the segments to be used. Then stabilize just those segments independently and load them into the final build. Experiment with deshaker settings. NTSC has worked well here, even when the final export is to be PAL.
Stabilizing a twenty-minute mp4 went flawlessly, so it appears that the GoPro files don't play nicely with the deshaker at 1080. No firm conclusions.