...but all we've got right now is an unconfirmed result.

I guess if intense gravitational fields can bend light, then it's not too much of a stretch to say they can affect nuclear processes. For all we know, the changes in radioactivity are driven by gravity (or neutrino fluxes) or something else. What concerns me is that most of the metaphysics I've heard has always preached how the universe would be unstable or monotonic if any of the major physical constants differed by even a smidgen from its current value.

Now these guys tells us there is a possibility that fundamental constants vary in a sinusoidal fashion due to solar gravity fluctations, And that even miniscule changes in solar gravity appear to be highly correlated with measurable yearly radioactive decay rates. Hmmmm. If that's the case, then lunar tides, which are considerably stronger, should impose a diurnal beat on decay rates, right?

As for your multiversal speculations, I have a feeling if this research is confirmed, the results and implications will make even bubble universes and string theory seem positively mundane as a result. After all, anything thing that physically connects the realms of quantum physics (radioactivity) and General Relativity (gravity on astronomical scales) is automatically a Unified Field Theory Phenomenon.