Your counterargument is therefore not with the principle of Epistocracy but rather with the implementation. I've thought about this before and I think I have a way to construct the voting test in a way that is robust to being "hacked". Copy and paste to follow:
1. There is already a de facto voting test for some fraction of Americans. Its called the citizenship test. And I for one find it offensive to basic reasoning that some people get to skip the test by virtue of being born in the right place. From now on let's include 5 questions chosen at random from the citizenship test on every ballot. In order to prevent the citizenship test itself from being politicized, the pool of questions which might appear on the ballot shall be chosen from the version of the citizenship test which existed before the voting test was added to the ballot.
2. Each candidate on the ballot gets to choose 5 multiple choice questions. The questions must be directly relevant to the powers of the office. Eg you cannot use a question about TV sitcoms from 1950 as a proxy to disenfranchise by age. The veracity of the questions must be a matter of public historical record or a provable logical consequence of facts that are verifiable by public historical record. Eg you cannot ask an opinion question like "Will Obamacare destroy America?" but you can ask "In 2009 did blowhard.com publish an article which concluded that Obamacare will destroy America?". Any news source above some number of readers/viewers can submit their works to the Library of Congress in order to make it qualify as a source for the untampered public historical record. Legislative acts and government commissioned works are automatically part of the public historical record, except in cases that they are classified as state secrets. Eg you cannot use a record of a private conversation of FB as a basis for a public historical record, but you could cite an article from a tiny publication like Rotary Club Monthly (provided it also meets the relevance criteria). Questions must have either a numerical, textual, or boolean answer. The potential answers to questions with numerical answers must differ from each other by at least 10%. The potential answers to questions with textual answers must not have more than 50% of the words in common. Boolean questions can be mapped to numerical or textual questions by asking "which of these statements is true" and then making the question one of the answers. The criteria on numerical and textual questions shall apply to the mapped boolean question. The courts shall approve the veracity and relevance and answer set of questions beforehand, and disagreement with the court decision may be rectified by the usual appeals process.
3. The last part is how to make use of the test results. This is a risky challenge as if there is a simple cutoff score then it is easy to make questions that disenfranchise the majority, and then the minority of the voting minority could always vote to empower itself further by raising the cutoff higher still. Thus there's a potential runaway feedback loop where eventually Democracy is abolished. I have two solutions.
3.1 The scores are aggregated and the bottom 20% are disenfranchised no matter the raw score.
3.2 No one is disenfranchised per se. Instead each vote is weighted by its test score. Each correct answer counts for 1 point and each incorrect answer counts for -1/n where n is the number of wrong choices. A voter that is systematically wrong on every question is probably wrong about their choice for president, so their vote counts negative (which is technically not disenfranchisement). A voter that gets a score near zero is no better than a random guesser thus they add no information to the system and so the system ignores them. A voter that gets every question right knows what they are talking about and so the system gives their voice the most weight.
Edit: Currently editing. I'm adding some after thoughts right now on scenarios where candidates/parties try to attack this and how my proposal is robust to those attacks.
Edit: Demonstrations of robustness.
I think these scenario's are exhaustive but I don't have proof.
0. The people making the test aren't objective (aka the primary criticism of Epistocracy). The citizenship test questions are objective because those questions were made long before my proposed system and the people making them didn't know those questions would be used for this purpose. The questions chosen by the candidates are biased, but they are biased in a way that exactly cancels out so that neither party has an advantage. The possibility of disenfranchising most/all is addressed in section 3.
1. A candidate leaks their answers to their base of voters. This is improbable as keeping everyone quiet would require a voter-base sized conspiracy.
2. A candidate picks questions which pander to biases. Eg "True or False, Democrat XYZ proposes to give free healthcare to illegal immigrants?" The system is robust against this because the question could have actually come from candidate XYZ (who knows he never said such a thing) as a way to lower the opposition voting weight or the question could have come from opposition candidate ABC because he knows his base will think its true. A voter that does not truly know the underlying information is equally likely to increase or decrease the weight of their vote by guessing based on their biases. The only way to have weight in this system is to be an informed voter.
3. A party props up an irrelevant 3rd party in order to pack the test. The first problem with this is that if you prop up another candidate that's similar to your own, you risk splitting your own vote in two. The second problem is that the marginal benefit is 50% of the questions are favorable to you (and 25% neutral) instead of 33% (and 33% neutral). So doing this may tip the weights, but it certainly doesn't guarantee you a win. The marginal benefit can be further reduced by upping the fraction of neutral questions. The third reason this attack doesn't work is either party can do it. There is no asymmetry that one party can take advantage of. At best you get away with it for one election cycle until the other party starts doing it.