"must outweigh familiar, atomic, matter by about six to one" but despite our best efforts it cannot be detected but there's vast amounts of it.
It seems to me there must be a better explanation because so far this one (i.e. it's there but we just can't detect it at all) just doesn't make sense.
But you should know that this is precisely the same response that scientists took to dark matter. They have spent decades doing numerous studies and experiments trying to nail down the source of these unusual observations that might be "dark matter". And in every single case, again and again they've eliminated everything else it could be and focused in on a very tightly constrained explanation: weakly interacting massive particles traveling at very sub-relativistic speeds (aka "cold dark matter"). The dark matter/WIMP theory has now been verified to an enormous degree across a variety of different observational fronts. Nothing else fits the bill no matter how hard we try, only a very specific dark matter theory fits the evidence.
And it's not unprecedented, we know of other types of dark matter (such as neutrinos) though we know such things don't make up the bulk of the mass that appears to be out there. We have detected it, time and again, we just haven't observed it directly. Nor do we know exactly what it is, though we have some strong suspicions based on likely extensions to the standard model.
There really is no better explanation.
The most visually striking evidence comes from the Bullet Cluster. We can see two galaxy clusters that have recently collided at ~1% of the speed of light, causing the gas to be slowed and heated. And we can map the mass distribution via gravitational lensing, and see that a large amount of the clusters' mass has passed right through each other without being slowed. This is more or less what you would predict if "dark matter" is made of weakly-interacting massive particles (WIMPs), and is pretty hard to explain by appealing to a modified law of gravity.
But we have detected it, to the best of our present capabilities. We've measured how much baryonic matter are in formations, calculated how much mass is needed to keep the structure together and spinning, and come up short. That shortness is dark matter. It's sort of evidence by absence. There is something there that has mass but doesn't experience EM forces.
Either that, our our theory of gravity is wrong on a very fundamental level. On proposed alternative, that describes the motion of some stars without missing any mass is MOND: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
The problem with modified gravity, is that it requires a lot more theoretical complexity to explain observations like the Bullet cluster and galaxy rotation, and the large-scale distribution of matter in the observable universe. Ie. a modified gravity theory that works for one of those observations, fails for others. Slow, massive dark matter clouds explain all of them quite nicely.
another problem with MOND is, that it is in my opinion and a friend of mine that is more deeply into logic, not a classical logical explanation. We have no prove in a logical sense yet, but we both had the feeling that you need some more complex logic to get satisfy the max function in MOND. I asked my old logic professors, but did not get an answer...
For a long time I also subscribed to the idea that the missing matter was better explained by faulty math, somewhere, but as our observations get better it's looking more and more like there's really something there, that behaves independently and differently than the matter we know.
I just wonder if it isn't a side effect of some other (not understood) aspect of the universe rather than the result of the behaviour of some particle.
To illustrate, gravity per se doesn't exist, it's the outcome of the bending of space towards mass. So it's effect is real but it's not because some sort of gravitional particle is acting.
Keep in mind that virtually every way we have of detecting things involves electromagnetism. If there were to be some form of matter that does not interact with the electromagnetic force, then there would be very few ways we could actually detect it, gravity being one of them.