Eric, you wrote:
"Change the Coulomb barrier width a small amount, and out of the calculation comes an alpha decay rate that is different by some orders of magnitude than it would otherwise have been."
Any example on that?
Please note that my simplistic argument implies that there is no net Coulomb barrier since the protons push more outwards than the electrons pull inwards so it is more like a Coulomb ditch. Of course, that is not to say that e.g. removing the electrons would not speed up the decay. The question is, with how much.