It seems that prudential reasons are intimately tied to what we want in some manner that moral reasons are not. I hope to show that this claim is false.
Sounds false to me. I guess the putative "tie" could go in either direction: from 'wanting' to reasons, or from appreciating reasons to 'wanting'. But in neither case does there seem anything special about prudential reasons in particular.
From 'wanting' to 'reasons': A desire theorist may think that prudential reasons are given by what we would ideally want for our own sakes, or something along those lines. But then they will presumably give a similar analysis for moral reasons, only with a different restriction (or no restriction at all). Some idealization is necessary, of course, because our actual present desires may not suffice to ground either morality or prudence -- cf. future Tuesday indifference.
From 'reasons' to 'wanting': We can imagine an 'aprudentialist' who doesn't care about his own future welfare, just as we can imagine an 'amoralist' who cares nothing for the welfare of others. Normative reasons are never guaranteed to be motivating -- agents may be irrational, after all, or simply act on desires which aren't guaranteed to align with either prudence or morality, as noted above.
Moreover, the impassioned may care more about loved ones and valued projects than they do about their own welfare, in which case (some) moral reasons may have greater motivational force than prudential reasons. In this case, the motivationally significant distinction is not between prudential and moral reasons, but between internalized and merely recognized values. The latter are experienced as 'alienating', insofar as they place demands on us that conflict with our internalized 'wants' or preferences. Now, it happens that most folks have internalized their own interests but not everyone else's, and hence it's only moral reasons that they experience as alienating. But don't forget that some moral reasons may also stem from internalized values, so not all will be alienating in this way. And even this limited connection is a merely psychological fact, of no great philosophical interest.
Overall, I'm pretty skeptical of the distinctive philosophical interest of prudential reasons, or of any similarly restricted class of practical reasons, for that matter. Any apparent interest to the prudential-moral content distinction may be better captured by the distinction between internalized and uninternalized (alienating) values.
See also: Moral Roots and Alienating Aspirations.