My comment to the question notwithstanding, it seems that when faced with this difficult choice, the majority have gone with the me + am version...
Be a guide to me who am empty of every good work.
You alone, O Jesus, are everything to me who am all yours.
Come then to me, who am a midwife
There are at least dozens, if not hundreds of similar forms in Google Books. Admittedly, most of them are old (and of course, there's no way of measuring the vastly greater number of times writers have simply rephrased to avoid the problem). But it's a "vote of confidence" of sorts.
Per @Colin's comments above, I don't think there's any doubt that strictly speaking, there is no other grammatically valid alternative. But obviously no-one much likes it, so we usually rephrase.
Since I hold him in such high regard, I must just cite Daniel Defoe's 1719 Robinson Crusoe...
in common justice to me, who was a considerable owner in the ship, the could not turn me as it were out of my own house.
...to show that me has to be right. It just works better with a past rather than present tense verb.