I thought the Syrian community only accepted sincere converts for whom marriage/a relationship was not a motivating factor. According to the Wikipedia article on Syrian Jews:
Based on these standards a goodly number of converts have been accepted into the community. Genetic characteristics play no role whatsoever.
Sincerely,
Moshe Shamah Rabbi, Sephardic Synagogue 511 Ave. R
Brooklyn, NY 11223″
Rebdoniel, how have things worked out for you?