Thanks for collecting all those links, Moma! You are ever the font of research :-)
As I said in the other thread (
http://www.newagefraud.org/smf/index.php?topic=1527.0;all), I've been very involved in researching this stuff, and you are correct: Though some tradition of sweating existed in Gaelic areas, and in Portugal
http://algarvivo.com/arqueo/ferro/alto-das-eiras.html what we know of those traditions is nothing like Inipi.
The information we have on the Gaelic sweathouses is that they were made of stone (many still stand, as seen on Anthony's page). A fire was built inside them, heating the entire structure. Once the stones of the building were sufficiently hot, the remains of the fire on the floor inside were swept out, and we have accounts of a person lying down inside on a bed of rushes, and praying or contemplating till they "reach a state of peace." As chinks are part of the structure, both due to the realities of building with stone, and due to the need for smoke to get out and air in, the experience would not be in total darkness unless performed at night. The structure recently restored in Portugal is very interesting, and consists of a stone structure much like the Gaelic one, but later (probably after Roman contact) augmented with additional spaces more resembling a Roman bathouse, yet still with Celtic-type iconography.
Anthony thinks psilocybin may have been involved, but I don't personally think there is convincing evidence for that. There would be room for a few people to sit in one together, but I'm unaware of any accounts of that. It is possible that the structures were built after contact with Scandinavian peoples, so if any rituals connected with them resembled another culture, it would be to those cultures. However, sauna ceremonies that I know of are almost always communal, so that's a significant difference.
There are similar stone structures built here in New England, but no surviving knowledge of who built them. As the local Indigenous folks say they have nothing to do with them, the current archaelogical theory is that they were built by Irish or Scottish people who came in the usual waves of invasions/immigrations. I've been in one of these, and would concur with this.
There's one account from Martin Martin of a hole being dug in a floor and a hot "quartz rock" being used to create steam, with the affected part of the body held over the steam, but here we find even less about a ritual or spiritual use.
The first reconstruction at a Burnt Mound structure, that I know of, was by archaelogist Michael J. O'Kelley. (account and pictures in O’Kelley, Michael J., 1989. Early Ireland – An Introduction to Irish Prehistory. Cambridge University Press, Cambridge. pp. 223-227). They did not approach the site with preconceptions, except perhaps that it was used for cooking. This is reasonable as some of the surviving local names,
fulacht fian "cooking place of the warrior band" and
Fulacht na Mór Ríoghna - "the cooking pit of the Mórrígan" would indicate as much.
For the Ballyvourney reconstruction they put long poles in the remaining holes, resulting in a tall, conical shape. I think it more likely that, like more permanent houses of the period, the poles should have been placed straight up and a roof constructed separately, such as seen in roundhouses or other thatched structures. Again, no evidence of an Inipi shape at Ballyvourney. The cooking went quite well, though :-)
From the evidence I think it's likely they were like an outdoor kitchen and/or bathing area - I think the water pits were likely multipurpose, quite possibly used for bathing at one point, and dying or brewing or cooking at another. The pole holes do not surround the water pit in the digs I've seen. The Ballyvourney structure has an additional, small hearth inside the ring of pole holes, but it is off to one side. There is no central pit. The fact that there is no central hearth, as is found in Irish dwellings of the period, would argue against the poles being used to make a dwelling of any sort. Also the alignment of what would most likely be the door does not line up with Irish dwellings.
The Fulacht Fiadh article I co-wrote on WP is not too bad:
http://en.wikipedia.org/wiki/Fulacht_fiadh During my late teens and early twenties, I attended some ceremonies in the Neopagan community that were basically Wiccan rituals in an Inipi structure. That's what the people doing "Celtic" or "European" sweats seem to all be doing. I have to blushingly admit, back then (early eighties) I even designed an alternative to these things, along with some other women, where did a sort of collective thing, based even less on Inipi. Still, I was young and ignorant, and once I learned more about the traditions and views of Native peoples, I stopped even doing those.
In more recent years, I got pulled into an effort to see if we could reconstruct a more authentic, Gaelic sweat ceremony, based on the actual fragments we have, additional archaelogical reconstructions, and comparisons to surviving Latvian sauna ceremonies. At first I was game. But, to my great dismay, I discovered the main person I was collaborating with just wanted to find "Celtic" ways of doing Inipi. She didn't care that the surviving fulachtai fia sites, and stone sweathouses, do not have holes in the center for rocks, as well as other details you posted above that differentiate them from Inipis. Like the Birmingham crew, she came at it with the expectation we'd find "Celtic Inipi", and so ignored whatever contradicted this, and exploited what few similarities there are, including wanting to alter things to better fit her preconceptions.
Due to her insistence on appropriating Lakota ceremonies (
http://erynn999.livejournal.com/250303.html?thread=1724095#t1724095 ), I won't be collaborating with her in the future, and am dismayed I ever trusted her (we even co-authored a book together). Much to my horror, she is now using some of my research, and even things I stupidly told her, as a point of comparison, about Inipi and Sauna. It was, and is, a heartbreaking situation.
What I have seen over and over with this stuff is that people who want to rip off Inipi think it's somehow ok if they can call it by a term used by another "white" culture. But ripping off and misrepresenting Gaelic cultures isn't cool, either. More of our stuff is public, and in order to rebuild things we've had to share more publicly than I'd like, but that doesn't mean people can make stuff up and call it Gaelic or Celtic. And it's certainly not ok for them to do that and think that tossing a tartan blanket over a sweatlodge makes it ok to rip off First Nations ceremonies. When they do that, all they show is their blatant ignorance of the cultures of the First Nations, as well as those of the Celtic Nations.