Same problem though, the fact that the "token" is pre-issued vs election-specific doesn't change anything.
If you are worried that the government is going to change the vote tally, should you not also be worried that the government will generate fake keys to vote in the election, or simply add rows with fake signatures? You need to verify that those rows are authentic, and that's not possible while maintaining a private ballot. The only defense is to have someone who can say "I.C. Wiener is not a real person", whether that's the government or the public.
Private-ballot voting only works with the government as an "oracle". The government is the defense against sybil attacks (multiple voting, etc). You can have other systems if you are willing to let people see how each other voted, but private-ballot voting is pretty ingrained at this point.
--- theory stuff:
A trivial solution to the problems that blockchain approaches is "majority-wins". You take a vote and whatever the most participants agree is the "true" history wins (eg electing a master node in a distributed system). But how do you prevent one attacker from pretending to be a lot of people (aka a sybil attack)?
What blockchain provides is a solution for sybil attacks - participants are individually financially incentivized to burn the maximum amount of power they can, and an attacker must burn more than the rest of them combined to succeed.
As a general statement, "private" blockchains make little sense in that context, since you've removed the Red Queen's Race that provides the sybil-resistance. Most people are better off just using a database, since they really have no need of sybil-resistance anyway. The participants are trusted (f.ex when electing a master node in a distributed system), or can agree to trust some oracle (the party who runs the server). A regular database works fine for these cases.
Without the cryptocurrency attached, what you really have is Merkle trees, not a blockchain. I love Merkle trees, I use them all the time in my filesystem (ZFS). But the "shape" of the data on disk does not provide any particular benefits in terms of consensus-resolution. For things like voting, distributing the vote tabulations as a flat CSV would be just as effective as distributing them as a Merkle tree.