Whenever this comes up, I've been saying that a True Moral Theory would not prevent the asker from repeating their question. Instead it would show the repetition of the question to be absurd after a certain depth of explanation.
If the Mafia is trying to assassinate Louis Griffin, she can explain to Peter why he should care. But, Peter can always say "so what's it to me?" Or as Russell says,
if he ultimately doesn't [care], then there's ultimately nothing more we can say.
And here we are supposed to believe that moral theory X loses its claim to objectivity.
But the "force" of morality comes not from its compelling people to see the light, or (as some of Ophelia Benson's commenters seem to believe) intervening as if it were a force of nature and preventing an immoral activity. The "force" comes from its universal and consistent application. People who choose not to act morally according to the theory cannot escape being labeled "morally wrong" by that theory. In that sense it is inescapable.
The meaning of "flashlight" doesn't break down because you choose not to build one. An instruction manual on how to build flashlights doesn't need to include a section persuading people that they should build flashlights. Perhaps it would if they want to sell their manual, but the section would have no bearing on whether the methods were correct.
Similarly I don't think an instruction book on morality needs to include section on why you "should" behave morally in order for it to be morality.
I do think, most of the time, people who might consider themselves amoral, or ambivalent or otherwise hard to pin down, are actually moral in a conventionally acceptable way after all and don't realize it because of fuzzy thinking. For them you actually can build a bridge into morality, because, with eloquence, you can reveal the pre-existing concern for moral issues they already have.
I don't mean to sidestep the problem. Just, I think most people who would count themselves as instances of the problem aren't, and most things people would point to as instances of the problem aren't either. And most of these, I think, contribute to our belief in the significance of the problem. If this point could be well made I think it would alleviate most concerns we have with what morality is.
For the true believers, the case is tougher. I don't see that any "should" can lead in to morality from without.
If any kind of bridge could be built, it would have to be from within the preexisting interests of the person who is still on the fence about whether they should be moral. But then, you are appealing to them on the basis of something other than morality. If someone truly doesn't share any of the interests embedded in the moral theory, you cannot persuade them without changing their interests. But it is wrongly expected of morality that it should concern itself with appealing to the self-interests of particular individuals.