The problem here is that each deliberating agent is an individual, not a collective, so it isn't clear why their decision must be governed by collective rationality. From the viewpoint of the individual, the Hobbesian choice is a false dilemma. Their choice is not between a world of total morality or total amorality; all they get to decide is their own actions. And, as in the prisoner's dilemma, the individual is better off acting prudently no matter what the others do (assuming their behaviour is independent of the individual's decision). Collective rationality advises even the egoist to behave morally; but individual rationality need not, and it's surely this sort of rationality that aims to guide the practical reasoning of individuals.
David Gauthier (Morality and Rational Self-Interest, p.19) presents the incompatible arguments as follows:
(a) If it is reasonable for me to accept only self-interested reasons for acting, then it is reasonable for everyone. But if everyone accepted only self-interested reasons for acting, then everyone would do worse than if everyone also accepted moral reasons for acting. But it is not reasonable for everyone to do worse than necessary. Therefore it is not reasonable for everyone to accept only self-interested reasons for acting, and so not reasonable for me.
(b) If it is reasonable for me to accept moral reasons for acting, then I must do better by accepting them. For it is not reasonable for me to do worse than necessary. But whether others accept moral reasons or not, I do better to accept only self-interested reasons, rather than moral reasons as well. Therefore it is reasonable for me to accept only self-interested reasons for acting.
Both sound fairly compelling, though I also think both arguments are flawed. (b) neglects the good to/good for distinction, which I think is a clear mistake. A person might reasonably sacrifice their own interests for the sake of some good which they value even more highly (e.g. the well-being of those they love). But we may fix this problem by modifying the argument in (b) so that it is merely talking about what is prudentially reasonable. After all, the Hobbesian argument is that it's in everyone's interests to be moral, so the amoralist need only deny this much. Given this modification, I think their defence is a success.
(a) shows that rational egoism is what Parfit calls "directly collectively self-defeating", defined (for any theory T) as follows:
if we all successfully follow T, we will thereby cause the T-given aims of each to be worse achieved than they would have been if none of us had successfully followed T. (Reasons and Persons, p.55)
However, rational egoism makes no claims to be a collective theory. Rather, it is a theory about what it is rational for an individual to do. And as Parfit notes, it cannot possibly be directly individually self-defeating, for by definition, if an individual successfully follows rational egoism then he will have achieved what's in his best interests. (Of course, it might be indirectly self-defeating, due to the paradox of hedonism. But that would simply show that the individual had not successfully followed the theory. The theory would tell him that the prudent thing to do is make himself less disposed towards selfishness, and the egoist failed to do this.) So rational egoism is not self-defeating in any theoretically problematic sense.
So, does collective rationality have any practical import? Well, it does when we are making collective, i.e. political, decisions. We can concede that an egoist may have no (individually rational) reason to behave morally, without that diminishing the importance of morality more generally. For even the egoist must agree that it's best for all involved (including himself) if others are moral; and he should even agree to civil/political measures that would help promote the formation of moral character generally - even in himself. If the measures caused him to acquire a more moral character, this 'cost' (in individually rational terms) would be more than offset by the benefits of having more moral neighbours. Rational egoism implies that the rational thing to do is encourage the "irrationality" that is morality.
This is a less than satisfactory answer. It still allows that the egoist should try to encourage everyone else to be altruistic whilst secretly remaining selfish himself. But then, it shouldn't be surprising that one cannot provide a full defence of morality from within the framework of self-interest. What we really need is a more neutral battle-ground, a way of judging between the rival frameworks of self-interest and morality, without presupposing either.