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 (e.g., see the interesting comment by cnread below). It also seems to be case that meo quidem iudicio can be put in parallel with meo quidem animo, where quidem also stresses that the uttered state of affairs should not be interpreted as a fact, but as the speaker’s opinion, leaving room for disagreement. For example, I've just seen that meo quidem animo is translated as 'to my mind at any rate'.
I agree with cnread's remark below that "the difference from saltem may be that saltem limits the whole clause, whereas quidem limits meo specifically (as word order also suggests)". I also buy cnread's translation: "At any rate, in my judgment, I have shown clearly enough...". Note that the emphasis on "my" already captures the emphatic affirmative meaning of quidem, whereby it is not necessary to translate it (cf. the stilted transl. "At any rate, at least in my judgment, I have shown...").