How can one reconcile the desire of a married man to marry a woman who has recently converted to Islam, with her refusal to be a second wife, coupled with his fear of her apostatizing from the religion if the marriage does not take place?

You must sever your emotional relationship with this woman. If she agrees to polygyny, that is good; otherwise, you must leave her, explaining to her that your religion commands you to do so, and that there is no relationship between men and women outside of marriage. You can connect her with righteous women who can guide her to what is good.