Having been a missionary to a Buddhist country, I understand your query. We wish to reach even the Buddhist priests. The problem with your scenario, is that I have never found false religionists to be open to the Gospel message when they are practicing their own religion. For example, once down in Tokyo a friend and I saw a Shinto priest sprinkling "holy water" around his shrine. My friend and I approached him and tried to just give him a tract, but he totally ignored us. Again, I have discoursed with Jehovah's Witnesses coming to our door both in the US and in Japan. I've never convinced a single one. Another time, I met an "Aum" cult adherent giving out literature, and he turned his back on me when I tried to give him a tract. I will confess, though, that I once came up from behind on a Zen priest out on his "alms" mission, and stuck a gospel tract in his alms bowl.
On the other hand, I once had a young Buddhist priest who had fled the temple come to my church service. He was staying with one of our men, having fled the temple because his father was trying to force him to marry someone. He listened very carefully to the Gospel; didn't get saved that day, but he was open. So the best time to approach a religionist is not when they are doing what they think is their duty, but when they have free time. Otherwise, I try to stay away from Buddhist priests and the like so I don't lead others to think their work is moral. So I've only been in a Buddhist temple once, and that was when our mission director came over from the US and wanted to see one.
Keep up the good work.