Hi Angel,
I know these references for having worked on them for my memoir and now starting a PhD project about contemplative practices using, probably, an interview method based on micophenomenology to get some info about the long term changes in the experience of advanced meditators from different traditions.
Michel Bitbol, who is a main co-author of the article you mention, is part of my PhD committee that i'm starting this year. I'm probably gonna train in Microphenomenology with C. Petitmengin, although she's retired now, so I'm not sure it will be her who does that.
(((((As you seem interested in all that, if you can read french, I suggest reading Bitbol's book "Does consciousness have an origin ?", it's not translated that I'm aware of. He draws parallels between phenomenological practice (épochè and transcendental reduction and contemplative practices including vipassana, shamatha, and open awareness stuff, and argues that it would be smart to consider them as forms of phenomenological reduction rather than the other way around.))))
Anyways, here's my take on this - hope it doesn't sound too blunt , nothing personal.
These methods don't add much, if anything, to actually meditating. Nor does neurophenomenology (Bitbol thinks neurophenomenology doesn't add anything to introspection. Neither does my adviso Jean VionDury who is a career neurophysiologist. That's from a fundamental, transcendental epistemological POV, we might say, as in : it's principally impossible, because of epistemological reasons, that studying the brain will add understanding about what happens in meditation, because meditation is not happening in the same domain as any conceptual construction ; "the small mind can't explain the big mind". Furthermore, even within the epistemological framework and assumptions of neurophysiology, fMRIs, as chris pointed out, are not precise tools at all...)
The reason people are inventing methods like "microphenomenology" or neurophenomenology to study metditation is, rather, to try to find ways to get these topics inside the range of mainstream science, which is dominated by certain epistemological values and rejects anything which cannot be objectified in scientific terms. Plus, technology is impressive and cool, etc.
Sad but true.
A lot of research, actually, most academic research, is based on where the money is. These days, you have 10 times more chance of getting some money to do research, if you plan to use MRI's and the like. Most professional researchers spend more time trying to get grants to do their work, than actually researching. ...
Try to get a grant from Mind and life to do research on contemplative practice : most are attributed to people doing neurophenomenology. Because, tada ! The founder of M&L is Varela, who invented the neurophenomenology thing, and managed to become influential and attract investors, prompting, ... etc. The first paper you mention was funded by M&L, actually.
It's all about the dough, my brother. And politics. Although the intentions are certainly honorable. But it's about the dough and the general landscape of academic research...
I mean... Most research on meditation is on MBSR. Mindfulness is JKZ's private brand. This guy is worth 45 millions last time I checked for having rebranded the Satipatthana sutta for his own benefit. Pretty clever ;)
Also, these guys are not awake, for the most part. I don't know about Bitbol, he seems very deep, but for having discussed over lunch with him, and for other reasons, I'm not sure he's as advanced as many people on this forum and beyond, although he's definitely brilliant and somehow illuminated.
So, I suspect that what daniel is trying to do with these projects, although I can't be sure, is just to help make all this mainstream, using the dominant worldviews and truth-values of the culture of the day, in a characteristically pragmatic fashion... I hope, at least

I suspect that, because these are precisely the reasons why I'm chosing these methods in my PhD project : (1) More chance of getting money if I use a method validated by the scientific community (it sounds more serious to the guys in charge

) (2) This as a doorway to get the deeper end of these topics into the public arena.
But I have absolutely zero expectation that this adds much to actually practicing and reading the old texts and honestly, I think it's a pain in the ass that we have to go through this kind of thinking, but hey....
edit : The benefit, in my eyes, is pedagogical, ie., the wise have always said the same thing, but they always had to find new ways of communicating it with their peers. (!! inflated ego alert !!)
Also I don't have much hope that it will have a lot of impact... I think the important stuff happens outside these institutions... and that this will be the trend in the coming decades, more and more. For instance, the DhO is perhaps making more for the advancement of meditation than all the M&L research put together. I would bet my money on that, anyways

Last point, which I submit to your appreciation :
Could this be what the buddhas and jesuses did in their time : adapt and present their insights to fit the worldviews and values of the culture and time they were born in ?
What is the dominant worldview these days, at least for the minority of the world population which is not religious, but has all the academic capital, if we can put it that way ?
I leave this over to you for pondering.
Kind regards,
Olivier.