If you combine all the different NonDirective methods out there, you'll find quite a bit of research. I'll try to link to that here, as I can.
Since the core principals of the techniques are fairly similar (a point that would be argued by some of the organizations that teach it), you can fairly safely say that if one method of NonDirective meditation provides X benefit, it's likely that another method would provide similar benefits.
However, your mileage may vary, and I suggest that if you want X benefit, and you only see research done on Y method, and you dont think any of the other methods will do the trick, by all means, go with Y method.
Also, I know the information on this page is really incomplete, but I promise I will get it updated as soon as possible - however this might be in the form of more specific blog articles, so keep your eye on the blog.
This article talks about increased HRV during nondirective meditation, and therefore, a possible decreased risk of heart disease in the middle aged.
This article discusses the beneficial alpha and theta waves found during nondirective meditation.
Emotional / Stress:
This article discusses how nondirective meditation might assist with state and trait anxieties.
Specific Types Of Nondirective meditation and associated research
Of course the TM group has the funds to do the most research, which at times has brought that research into question, but you'll find that the studies are mostly well designed, and probably come from a good place, as far as intention.
To read about some of the research that's been done there, see the page on their site, below.
NSR provides a pretty low cost model, and has also done some research on their meditation. You can find that info below, at their site.
The ACEM method has done some research as well, and you can find it here: