There ought to be a typology of various kinds of unverifiable statements. I'm not aware of one though. The unverifiable statements that the OP has listed in his question I would suggest are in principle unverifiable. But there are other kinds.
For example, space had three dimensions. And we can verify statements about 3d geometry directly. In fact, this is why plane and solid geometry have been around for more than two millenia with their origins in problems of mensuration - the determination of areas and volumes.
However mathematicians have recently discovered how to think about higher dimensional spaces. These obviously cannot be verified in the same direct way. Instead indirect ways are used.
Now, does this give us information about 3d space?
Well, looking at 3d space compared to all the other spaces can tell us first, why it's special; and secondly, what it had in common with other spaces; this is useful knowledge.
Here's another example from physics. Hawking radiation has not yet been verified directly. This is not surprising given the nature of what is being asked to be shown. However it's based upon two very well tested theories - QM & GR, and so it's taken to be very plausible.
Notably it's a prediction, in the conventional sense of the word used in physics; unlike how Edward Witten, perhaps in a misguided attempt to market String Theory said it 'predicted' gravity and even coining a new term for this: a 'postdiction'; but in actual fact, it's merely a consistency test, and this gets it right; and it has been already used in this sense in physics; for example, QM had to be 'consistent' with classical mechanics in a certain limit.
Whereas D-Branes are physical objects actually predicted by String Theory. They are, like strings, not currently directly verified; and not likely to be so in the near future; but they have been verified indirectly by a consistency check: in that have been able to give a description of the Hawking Entropy of Black holes in terms of micro-states; and this is also a useful advance because the usual description of this does not use the conventional thermodynamic notion of micro-states. So knowledge is gained, even if it ultimately turns out that string theory is wrong.
So what I'm trying to show here is that there is a useful typology of unverifiable statements that would be worth theorising about and unearthing; if it has not been done so already.