unstated in the OP, but my supposition (reasonable, I hope), is that there will still be a limited number of congressional seats so that candidates below a certain popular vote threshold will have 0 representational power. in that case it is still in the best interests of voters to vote for someone who is likely to clear the threshold and not throw their vote away by voting for a perfect ideological match (i.e. themselves).
this seems fairly elegant to me except that it might lead to a neglect of the provincial concerns of low population density areas (which was a major concern of the founders), but on the plus side, those rural voters can at least find an ideological match even if they don't find someone to represent their geographic interests.
In all likelihood, a few people would get most of the votes, because they're competing for attention from a national audience. Therefore, it is possible that local issues get marginalized, so I think it would be necessary to give people multiple votes. That way they can split their vote and choose both national candidates and local candidates.
We can debate all these details when we get to the constitutional convention.