Among Bennett (§180), Allen & Greenough (§397b), and Gildersleeve & Lodge (§338), the last provides the most detail on this construction.
Two varieties are identified:
Definite: The Accusative of the part affected
Indefinite: cētera, alia, reliqua, omnia, plēraque, cūncta; in other respects, in all respects, in most respects.
The first ...
As for your 1st question, meo judicio is clearly ablative (cf. also meā sententiā). And, yes, you're right: this use is often referred to in Latin grammars as "Ablative of specification".
As for your 2nd question, the particle quidem has recently been analyzed as a marker of emphatic affirmative polarity. This issue seems to be more complex than I expected (...