Again, I think your focus is just a little off. Your imagining of them to be converted won’t help in their conversion, but prayer will. Rather than praying for what you want to happen for someone, pray for God’s will to be done. Recall the Lord’s Prayer: Thy will be done on earth as it is in heaven.
So when praying for your intentions, perhaps something like “I pray for XYZ to happen for so-and-so, if it be in your will.”
I think the method you are referring to is much like creative visualization, right? In that method, it is claimed that we hold the power to change people through our imagination (it’s been quite a while since I’ve encountered it, so I may be a bit foggy on specifics). As Catholics, we believe that God can change people with the assent of an individual’s free will. Intercessory prayer helps too.