You and Me both
You would use I for the subject of the sentence and not Me. The fact that the subject is plural is not relevant. The fact the the tense is past or past perfect or present perfect is not relevant. The inclusion of both is not relevant.
If we take the first sentence and discard words two through five, we are left with:
"Me have reviewed the fees."
Clearly this sentence both sounds ungrammatical and is ungrammatical.
The extra verbiage is masking the flaw to your "ear".
"Bob and I have both reviewed the fees." is the grammatically correct statement.
Allow me to provide a brief partial lesson in English grammar.
English has three cases (some might argue differently, but for all practical purposes this is it):
Nominative (in a general sense the active in the sentence). Nominative pronouns are: I, you (singular), we, you (plural), who.
Objective (in a general sense the receiver of the action). Objective pronouns are: Me, you (singular), us, you (plural), whom.
Reflexive (in a very simplified sense of when actor is also recipient of the action): myself, yourself (single individual), ourself (all collectively e.g a Union)/ourselves (all collectively e.g. Union members), yourselves (plural individuals).
One of the rules of correct English grammar, is when there is a list, as in the examples, the reference to oneself is always last. This applies to either case.
It should now be clear what is wrong with, "Me and Bob have both reviewed the fees." The list of nouns is in the wrong order, AND the wrong case has been used.