I want to sign a letter jokingly not by name, but by a personal pronoun. Is the signature a subject or an object? I feel like using object pronoun (me) sounds better, but why? The signature looks more like a subject to me.
Example:
Best regards,
I
or
Best regards,
me
And for more people signing the letter, following the rules from Which is correct, "you and I" or "you and me"?:
Looking forward to your answer,
John and I
or
Looking forward to your answer,
John and me
ADDED:
Based on the @wjandrea's comment under Peter Shors's answer, can the ellipsis
(This is) me (signing that letter)
be used as an explanation why the default pronoun is the objective case?