My wife is entirely supportive of my intentions, but she is currently unwilling to abandon the belief in "that man". Will the fact that I am married to a woman who is not interested in converting prevent me from being seen as an acceptable convert to Judaism?

You might be able to begin the process of learning but you will not be allowed to convert if you intend to live with a non-Jewish woman. The reason for this is that the essence of conversion is acceptance of the Torah's commandments including the prohibition against intermarriage. You might suggest that your wife study along with you. If at the end of the process, you would like to convert and she does not, you will be faced with a painful choice. Before you embark on the process you should consider if you are willing to be faced with such a choice.