Scalability of homomorphic tallying
I am not sure why you think that "homomorphic schemes and big integers are not a very efficient combination". In most homomorphic public-key cryptosystem, the message space is very large. For example, the Paillier cryptosystem (probably one of the most used for secure voting) has a plaintext space size of $2^{2048}$ with current security parameters. This allows for elections with a million voters and a hundred candidates. Moreover, the plaintext space of Paillier can be increased if necessary (interestingly, it can even be increased "on-the-fly" if the plaintext space size seems too short, without having to ask the voters to re-vote). With $4096$ bits, you can support twice more candidates, or a billion of voters.