I would definately argue induction, but that's just me. I wasn't aware that the model is considered out of date, what's the text, I'd like to read it? does it also question rationalising the stability of tertiary carbocations by inductive effects? If not, I would have thought that the door swings both ways.
I like your solvation idea though.
My reference: Carrol, Felix A. 1998, "Perspectives on structure and mechanism in organic chemistry", Brooks/Cole Publishing Company....
Here is a short review of the discussion in the book (in somewhat bad english due to a hurry):
The stabilities of carbocations from tertiary to primary, might be explained in terms of the model of hyperconjugation. The same reasoning is used for explaining radical center stabilities. Of course, this is one of many models.
Maybe (my thought) the hyperconjugation model might be valid for carbanions too. Because increasing the number of alkylsubstituents on an alcohol, is actually increasing its acidity in gas phase. So, alkylgroups is perhaps able to delocalize or polarize negative charge away from the center. Just like they stabilize carbocations through hyperconjugation. The effect of the alkyl substituents is defended by theoretical calculations.
Funny enough, in solution the acidity is opposite. Maybe because the solvation of the anion is overcoming the electronic effects because of an favorable entropy term in the solvation process. A large bulky molecule is demanding in the ionization process, more solvent molecules around the molecule surface: an unfavorable increase in order.
Just to add to the confusion:
The acidity in both gas and in solution for halomethanes is: CH4 < CH3F < CH3Cl
So it seems that we cannot use simple electronegivity values to predict the acidity.
Acidity, so it seems, is a better explained by polarization.
Doesn't n-BuLi form the kinetic carbanion not the thermodynamic carbanion.
But is the actually kinetic carboanion formed?
You have also some primary proton on the endocyclic allylic position.