The first and biggest problem with pursuing this point is that religious claims or truths do not require verification. If a religious authority makes any sort of pronouncement or claim it can stand perfectly well on their authority alone.
Yes, that may be true for religions of belief (ok, that's where the term religion originated in). And mere association also work there. And that is, what we're intoxicated with in the west, which is an easy thing to do, because those associations are the basic functions of our mind. And that's particularly why I have a problem with Buddhism as a religion. Because it then starts to behave like such an entity that proclaims facts that appear to not require verification. Then suddenly lineage and ancient books become more important than something else. But it is not true for all aspects of spirituality, when you split science to "find out how things behave which are observed beyond the senses" and spirituality to "find out how things behave between the one who apparently observes or even consciuosness itself and the senses".
And in my opinion, the latter is based on facts (observations written down), that what Buddha pointed towards, does indeed require verification, or it is useless. And not only verification. To whatever method there are a couple of factors:
1. Does it solve the problem? (yes, it does. although it's not a quick drug.)
2. Will the effect stay, i.e. will it be a permanent solution? (yes)
3. Will it eradicate the problem at the root, or down the symptoms? (it will eradicate the problem at the root)
4. Does it come with side effects? (not ones you care once the solution is applied, but you can decide what to do with it. If freedom is something you do not want to have in the first place, then that solution may not be for you. If you want to become free of this world, then it may be the only solution, though not the only road to nowhere.)
And as in science, Buddha laid down two things:
A. A model (which is called the four noble truth). Those were the observations he made, and I would really rather call them "4 basic observations" or "4 simple facts" than "4 noble truths" because the demystification in language does the thing wonders. Buddha, it appears to me, at that time was no longer into mysticism, but rather fed up with it because it did not lead him where he wanted to. To him the methods of mystics appeared to be extremism. So he was searching for something simple, and practical, and he found it.
B. A method (The algorithm to stop suffering). It's a prescription. His lab journal, so to speak. You're free to take it as "This is what I did, and what I'm convinced leads to the cessation of suffering, you're free to try it. If it works, good for you, if it doesn't, scrap it."
Is this non-scientific? Well, there are again a couple of points.
1. This is scientific in that he claims when one follows the method (does what he did), then one will obtain that goal. It's like saying sit down and hit some keys every day and eventually you will be able to type fluently with 10 fingers. That's what science does. This experiment I tried, please somebody confirm my observation. Often times in science only a small group can do that, because you need particular equipment which is not readily available. For Buddha's method all you need is already there.
2. Does this match the medical standards for a medication, where every drug has to induce the same effect in all people and verify by a double blind study? Well, problematic. First of all, it will lead people there at a different pace. Second, because it's interwoven with life, you cannot set up lab conditions for it. Some try by ordination or going into the forest, but since you carry your conditioning along and even those environments are not free from mental traps, it works for better or worse. It may be more or less difficult for some people. And some may not reach it within this lifetime because they simply cannot let go. Does that invalidate the method? Well, for them maybe yes. For the rest, no. Not everybody will be a concert pianist after all, even though we tend to like the illusion that everybody will be able to do everything if we only try hard enough. That western illusion is part of the problem. Trying "hard" is the problem. There's a subtle difference to that and "following through" or persisting in concentration. But if your knees are bad, you will probably not become a record jumper. Can everybody rest in pure consciousness? Well, yes, since consciuosness is already there and working the same for everybody or this couldn't happen. You just have to find the exit from the holodeck labyrinth of your thoughts.
3. Is this like a psychotherapy? Well, in my understanding it can be best compared to that when comparing it to science. Psychotherapy also involves decompiling your mental game and reordering it. It also brings you to some form of realization. But blinded by medicine, many have the illusion that they go to a psychiatrist, he talks to them, maybe they get some medication on top, and the problem will soon be gone. It is not that simple. You will have to do the work for yourself (you will not only have to do that to achieve liberation, but you will also have to do that in psychotherapy). For those who did not accept that, methods like hypnotherapy (oh please lead me there in trance and do something with my problem) or shamanism (dear shaman, do it for me within your own mental game, i believe that works) have been invented. Where there may be some effect from the belief that it works, there is belief involved in those systems. Oh, and for the rest, a ton of drugs are sold (which are necessary in some cases, when the brain chemistry simply does not work right, i.e. the body is broken, or somebody is so out of balance, that other methods will not help).
In Buddha's method, there's a simple invitation to try it out, the stages have been described, and you can opt out at any time. Either it helps you and you suffer less, or you're free to go.
So it is not a "believe that after your physical death you will be reborn in heaven, but there is no solution for the time before than simply believing". And as in science, we have a couple of people who said that they successfully recreated the experiment and its effects. They even smile and say everybody can do that.
It would be so cool if this basic message was more easily available, without all the mystic stuff around. But alas, part of it we carry in our heads, part of it comes from 2500 years of organization around it.
If you now ask me "which part of it is Buddhism"? Then nowadays I tend towards the organization part. That's when I claim I'm not a Buddhist. The eightfold path at some point implies leaving routines and tools behind. Understanding a simple model and following a procedure does not necessarily need an -ism. Even more, an -ism is usually something to be identified with, which is contrary to taking refuge in Buddha.
If you ask me "Does the method work?" Heh. As far as I followed it, yes, it does. Things do indeed lose their grip, and the phenomena described in consciouseness can be observed and worked with.