Yet others say 'and myself', but that seems just plain awkward.

No one else has touched on this. ``Myself'' is a ``reflexive'' pronoun. They are used only when the pronoun refers to the same thing as the subject of the sentence.

Thus, ``He did that to me'', ``I did that to myself', ``He did that to himself'', and ``I did that to him'', but not ``He did that to myself'', ``I did that to me'', ``He did that to him'' (unless the antecedents for ``he'' and ``him'' are different, in which case it would be probably be awkward unless spoken using fingers ), and ``I did that to himself''.

Note that the subject need not be another pronoun: ``Bob did that to himself''.

Edit: I stated a fact imprecisely, due to an initial glitch in my memory. Better get that checked.