This is not necessarily an answer, just adding to the questions, as I seek the answer myself.
For a testable hypothesis, we must clearly define what we intend to test for. I tend to find SGI members' explanation of chanting or its powers to be insufficient, superstitious or dissatisfying. To develop a hypothesis on what chanting does, we can source from Nichiren's writings. We could also ask a sample of practitioners what the effects are and perhaps test the 3 most common responses.
I would also be interested in testing "prayer" and determining where chanting ends and prayer begins. We could possibly need an alternate word for prayer in the Buddhist sense, as prayer to a Buddhist is not necessarily equal to prayer for a theist.
Then, we must construct a test. We would test the hypotheses. This is partly where I get hung up and would be interested in actual scientists conducting research.
One thing I think makes testing the realities of chanting difficult is this concept in Buddhism of manifest and latent effects. Say you want to test how fast someone can achieve a goal, by chanting or not chanting. At least if I test this as myself only, there's this problem: If tasked with the same goal, once while chanting and once while not, some things to consider. Either way, the second time would likely be faster, as I would have a previous exposure to the task, although some alteration (like making through a maze with the same distance and number of turns, but different arrangement each time) could reduce the effect of this. Also, there's this chance that the chanting wouldn't manifest in an immediate effect, remaining latent until some other time, possibly during a chant-free test.
So, I have this experiential issue. I really wish I could split my life in two, like a multiverse theory (which I don't really believe in), where one instance of me goes through life chanting and another instance goes through life not chanting. Then, examine each life at the end. Which is preferable? This isn't going to happen, so we have to test some other way, like having some kind of task performed, measuring the quality, speed with which the task is done. There are almost an infinite number of tests that could be performed.
One other problem I can see in testing is a "spooky action at a distance" concept. Like my desire to split my life, we could try to use perhaps twins who had been separated at birth (let's try to stay ethical?). However, like a split atom showing responses to stimulation of its distant counterpart, my chanting self or the chanting twin could affect the distant/separate counterpart. Can we account for this kind of effect in the test?
I'll outline a few variables that we could test:
- Short term task
- Long term task
- Neuro imaging (before, during, after chanting) [this is one of the more objective angles I'm curious to see actual tests on]
- Chanting "Nam myoho renge kyo"
- Chanting other Buddhist chants/mantras
- Chanting nonsense
- Chanting "negative" words/phrases
- Silently chanting any of the above
- Not chanting at all
- Chanting in front of a gohonzon
- Chanting without a gohonzon
- You could use other "objects of devotion" or focal points as well
- Frequency of chanting (once, twice, 3x daily, or more?)
- Duration of chanting (single daimoku? 15 minutes, 30 minutes, 1hr, 2hr, as long as possible?)
Not seeming a concept of Nichiren Daishonin; apparently originating with Lynda Johnson, is this idea of "making the impossible possible" (by chanting). So, we could test something seemingly impossible, like putting test subjects into a room, between two rooms. The room on the left has a candle. the room on the right has a matchbook. Both the rooms with objects are locked and generally inaccessible to test subjects. The test subject is tasked with lighting the candle in one room and they are made aware of the matches in the other room. I would consider this rather seemingly impossible. Then, how much time is given any subject? It could take months or years to develop the karmic energy required to achieve such an "impossible" feat, solely through the power of chanting.
My personal hypothesis at this time is along these lines. Buddhists are often said to be "practitioners". What exactly are they practicing? I would argue that chanting [anything] has the effect of "distraction". It might also be called "centering". Typically, the place we set to chant is a place of peace and security. Chanting, somewhat unlike meditation, helps "clear the mind" as you generally are focused on the chant, although chanting can become like second nature and we can chant without thinking about it and our minds may wander. But, I think that that is what the chanting "does", after some time we will likely realize that our minds are drifting and you can bring it back the centeredness, focusing again on the chant.
So, what does that translate to, what is being practiced? I think that the chanter practices centeredness or self-distraction morning and night (as recommended by SGI/Nichiren). When you encounter a frustrating situation in your daily life, you can basically stop yourself before reacting, chant in your head or out loud, essentially distracting yourself from the frustration, or simply centering/grounding yourself. It "snaps you back" to your Buddha place, gives you a brief moment to rethink your response, and allows you to approach the frustration from a more rational place.
I theorize that chanting any phrase can achieve this same result. I also theorize the presence of a gohonzon or any other object would not have a noticeable effect on the results (although it could depend slightly on the task at hand and also if objects that cause test subjects anxiety could produce some negative result in the testing as well), but having subjects "focus" on anything will help them to recollect their Buddha place and increase their focus rate.
I'm not exactly sure how to test that.
A few fields of science may be needed to make strong determinations.
Here's hoping a few scientists might actually be able to shed some light on the realities of chanting. It's good to see I'm not alone in these thoughts.
Disclaimer: I have had involvement with SGI since 2002.