Can we equate nucleophilicity and Lewis basicity?
I appreciate your perseverance to think so deeply about this!
But...Yes, you have overlooked the main difference between Basicity &amp; Nucleophilicity ,i.e., Basicity (i.e. Lewis basicity) is a Thermodynamic term whereas Nucleophilicity is a Kinetic term. But here you have compared them under the belt of only thermodynamics.
Basicity is measured on the basis of the stability of the species, whereas Nucleophilicity is mainly aimed at the 'donating ability' of the species.
e.g. In polar protic solvents, the order of nucleophilicity in case of halide ions is:


  $\ce{F-}$ &lt; $\ce{Cl-}$ &lt; $\ce{Br-}$ &lt; $\ce{I-}$


Which contradicts with the basicity order.

Whereas in polar aprotic solvents, the order is:


  $\ce{F-}$ > $\ce{Cl-}$ > $\ce{Br-}$ > $\ce{I-}$


Which follows the basicity order.

I hope this might help you facing your confusion a li'l more logically!