Wow, that MicroMark tool looks very nice! I have never seen it in action, we use only traditional soldering irons.
I had the same problem when soldering photoetch, sometimes the small parts were falling off, or moved from their positions, because the whole piece was heated up. My best advice is to plan strategically – what to solder and when. I had to do quite a planning even with these simple handrails. First, I locked the superglued piece into the vise on a way that only the top rail was outside. I soldered the joints, then moved the part and worked on the lower rail.
I will definitely read more about that resistance soldering tool, it looks very interesting! It might be a huge help for modeling.