Your third attempt was almost right. With the images you emailed me I was able to produce the expected result:
You should specify the CompositeOperator. I think 'Plus' is the one you need but feel free to try the other composite operators.
using (MagickImage first = new MagickImage("Source_img1.tif")) { MagickImage second = new MagickImage("Source_img2.tif"); first.Composite(second, 0, 0, CompositeOperator.Plus); first.Write("overlaid_img.tif"); }