Cost to convert one integer array into another
Let $\ell_{i}$ denote the number of digits in $a[i]$. Then the complexity of the naive algorithm as suggested by you is $O(\ell)$, where $\ell = \sum_{i = 1}^{n} \ell_{i}$.
Moreover, the algorithm must visit every digit at least once. For the sake of contradiction, suppose the algorithm did not visit some digit in the array. Then an adversary can modify the unvisited digit to a different digit. This will prove that your algorithm's output is incorrect. Therefore, any correct algorithm must require at least $\Omega(\ell)$  comparisons. Thus, you can not expect better than $\Theta(\ell)$ complexity for this problem.