Should I interrupt a prayer that I intended as obligatory when I am assailed by the thought that it is a Sunnah prayer, or should I complete it based on my initial intention?

The cure for obsessive thoughts is to turn away from them and pay them no mind. Therefore, you must ignore the obsessive thoughts that come to you regarding the intention for prayer, continue with your prayer, and proceed on the basis that it is the obligatory prayer, not caring about the obsessive thoughts that afflict you. Otherwise, you will fall into a great evil.