Well, I'm just a simple layman with no relevant expertise but here's my first thought; maybe someone better trained in physics could expand on it and word it more clearly (IF it makes sense at all! :-) ):
I believe there has been quite a bit of research into this already. Apart from the natural reactor example, mostly research based on astronomic observations of the fundamental properties of very distant and old objects (?).
I think the confidence that scientists have in these observations (that they support U) is caused by the fact that they don't show something obviously weird.
I U was incorrect, I would suspect almost certainly some very obvious "weirdness" would be the result. And the reason for this is that so many physical parameters and phenomenons depend on each other. Small changes of individual parameters would easily have significant effects. UNLESS we suppose that they somehow change all at once and in perfect balance, such that for example in the case of the distant astronomical objects, we wouldn't notice anything unusual.
It seems rather unreasonable and unnecessary to take that possibility serious, because the alternative assumption (U) would be indescernable from this, and is strongly favoured by Ockham's razor.
I hope this makes sense. :-)
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