I really like your article. It confirms my belief that prayer is important and worth investigating. It did encourage me to look at some of the research you linked.
The Columbia research from 2001 about IVF might be something worth reconsidering citing. The history around it seems sketchy at best. Apparently the head researcher was a rather successful conman. Here's an article from Washington Post about it: https://www.theguardian.com/world/2004/may/30/research.religion
That being said, that doesn't change my opinion that prayer is a good and possibly influential thing. :)