We all must examine our own hearts but I would not be so quick to say that the failure to engage a mormon missionary is a sin. I live in a large Mormon community and my family does witness to the mormons in our daily lives of walking amongst them. I have had them in my home for Bible study, I have talked to them one on one, and preached to them at my church. But...
After years of observation I have noticed something. When those two young missionary men come to you with their neckties and books in hand, they are bringing a different gospel. They are false prophets and although it saddens me that the old men 'pass their children through the fire' in this way, they need to be seen for the dangerous evil that they are. Seeing how they are young false prophets, 2 John might apply and to even bid them 'Godspeed' would be to partake of their evil deeds. In fact, every argument or scripture passage that you bring will be noted and taken back to the bishop for the purpose of creating a better mormon argument for use on some other victim that might not be a strong and knowledgable as yourself.
I believe the best opportunity with a mormon missionary is to take them out of their 'official' capacity of false prophet and here are a some of mothods to try:
1) Make them take their ties off. Believe it or not, most of the time they will not do it. They may loosen them, but they will not take them off. The necktie is some kind of badge or official emblem that they are proud to wear. If they refuse to take it off then you know they are too proud to hear the gospel.
2) Those missionaries travel in pairs. Usually, one is the mentor and the other is a green apprentice. Try to identify which one is the apprentice and ask if you can tallk to him alone. They usually won't agree but the apprentice is usually scared out of his gourd and is in a better frame of mind to hear the gospel.
3) Those missionaries don't get out much but if you encounter them in the community when they are not on official business try striking up a conversation then while their guard is down. Ask them questions about themselves and try to establish a relationship and then see what the Lord does. Remember that it is charity that edifies, not knowledge.
Again, I am not condemning anyone on this thread but simply trying to point out that
maybe the reason Todd did not engage those false prophets is because the Lord did not want him to. No reason to beat yourself up. Plus, in light of 2 John, think about what you are modeling for your children. Do you want them to receive false prophets and listen to what they have to say?