I applaud you especially for the Chicago Tribune case. That hits all the marks of this case! Check the article below that specifically remarks on the rarity of murder by hanging in murder-suicide. It is unquestionable that the murder suicide explanation is a statistical long shot in the grand scheme of things.
https://www.ncbi.nlm.nih.gov/m/pubmed/21464696/
I still stick with the argument that statistically double murder is far more likely. Let's say this very bizarre type of murder-suicide is seen in 1 out of 1,000 cases of murder-suicide. Then, let's say that there are about 999 legitimate motives someone would have for killing a billionaire. Each of these motives involve an unlikely double murder with odds of about 1 out of 1,000. The fact is there is only ONE explanation involving murder-suicide, and it is a strange and unlikely one at that. Collectively, the many, many motives for murdering a billionaire greatly outweigh the probability that this was a very strange murder-suicide.