I finally got around to try Videomizer 2 by Engelmann Media. Not a good experience, it did already stall at opening the video clip with the GoPro video. I tried different formats, some opened and appeared to get stabilized, but export would only produce a sound file.
After I uninstalled Videomizer, Muvee's Turbo Video Stabilizer stopped working. Re-installing did not fix it, I had to do a System Restore to get it working again.
Speaking of Turbo Video Stabilizer, I found another oddity. I had a clip taken with an iPad and it was upside down. I used TVS to turn it around, but then it was mirrored(?), left side on the right- right side on the left. Maybe the fact that I had to add the .mp4 extension after .mov has something to do with it? This was the one thing that worked in Videomizer correctly, the clip got rotated and stayed in the right orientation.
I bought a 1 year subscription for Muvee's TVS. It costs $9.99 and you get all updates for free. It also works on my desktop and laptop, as long as I don't use them at the same time.