> would a speaker feel that that felt wrong, that it needed
> an indirect case, and shift it to the Dative?
> Interestingly, the Latin division of the prepositions
> between ablative and accusative neatly mirrors the
> division in German between dative and accusative, which
> lead me to this question.

I think ablative prepositions would shift to dative, since
ablative and dative were alike in the plural.

>  Secondly, when the meaning of a preposition shifts (e,g,
>  apud), would there be a corresponding change in the case
>  it governed?

Maybe. Cf. _zu_ which has shifted from genitive to dative.

/ BP