Below is my own version of your "Firefighter polishing the Fire Truck while people perish in the burning building" example of our responsibility to the lost. Ray's example shows how Christians' responsibility is to "stop talking about fishing" and go out and fish.
"By not sharing our faith we are like a man who sits down to a sack lunch amongst a group of those who are starving. He sits down, says thanks for the food, and enjoys his meal with his blinders firmly in place"
Below is my analogy explaining what a "fear filled" convert is.
"You are talking with some friends in the hallway at school when the class bully approaches. Out of fear you change your demeanor to that of submission, paying careful attention not to rouse the anger of the bully by the slightest bit of irritation. You walk on egg shells so not to deserve some form of torment from the bully to be meted out later on the playground. All the while you and your friends are secretly hoping that the teacher will hold him back a grade next year."
This type of convert is the product of Hell Fire preaching where the "convert" actually resents God for the punishment instead of fleeing to Him for the salvation from it.
Feel free to use them if you think they will help.