Like, I don't think something is moving but, yes, sensation can move or spread in a seemingly non-discontinuous way. Do you think we're describing the same thing?

I would very likely label what you describe as energy flow and I think most people who do energy work would do so as well.

That said there's a variety of different experiences of energy flow.

(Also, I'm more inclined to belief this is all in the brain's maps [electrochemical] than too much actually happening on-site [mechanical, mechanotransduction, or electromagnetic].)

Even with sight and sound there a lot happening in the brain. It's possible to have hallucinations in those channels. Energy perception seems to be more frickle and easier to mislead.

The problem with the "it's all in the brain's map" explanation is that it doesn't account well for effects one person causes in another person.

"Energy signatures" of removed organs on the other hand seem to remain from what I heard (not something I verified myself). That suggests that there a lot happening in the brain.

To me, this implies that the phenomenon is 100% psychosomatic and autosuggestive.

If there an interaction with the intention of healing, then there are certainly suggestions in place but that's not true for every experience. I have plenty of experiences where something surprising happened that I didn't expect.

https://scholar.google.com/scholar?q=therapeutic+touch

The first result I clicked on that list says:

An average 70% pain reduction was sustained over the 4 hours following TT, which was twice the average pain reduction following the placebo touch. Using a Wilcoxon rank sum test, this was statistically significant, p < .01. Study results indicated that TT may have potential beyond a placebo effect in the treatment of tension headache pain.

A bit further we get a meta-analysis concluding:

The review demonstrated that there are many approaches to therapeutic touch research, samples are described incompletely, and the therapeutic touch practices vary in the studies. Most of the studies supported hypotheses regarding the efficacy of therapeutic touch, though a number had mixed or negative results.

There also a huge difference between an effect being there and the effect being clinically useful. Kirsch et al (2008) might have found that anti-depressives on average don't provide clinically significant results, but that doesn't mean that the drug has no effects. Relaxing a muscle for ten minutes and solving the problem in a way that the muscle stays relaxed two weeks later are two different problems. Experiments with shorter timeframes are likely better if you ask a question like: "Does this do something?" as opposed to "What clinical relevance has the effect?"