Is it permissible to slaughter a calf as aqiqah instead of two sheep, especially if its value exceeds that of the two sheep, and this is due to the villagers' disinclination towards lamb meat?

If the calf is two years old or more, then aqeeqah with it is sufficient and fulfills the Sunnah, and earns reward. Some scholars are of the opinion that it is better than limiting oneself to a single sheep, just as one who performs aqeeqah for a boy with a single sheep still attains the virtue of the Sunnah. Therefore, if the calf has reached the aforementioned age, then what you have done is correct due to its greater benefit and people's desire for it; otherwise, the aqeeqah is not valid.