What is the right notion of security to use for file encryption?
Yes. $\:$ NME-CPA is such a notion, and is equivalent to modifying the IND-CCA notion so that

$\;$ the adversary can submit more than one ciphertext simultaneously
$\;\;\;\;$ and
$\;$ the adversary can only submit ciphertext(s) one time
$\;\;\;\;$ and
$\;$ that time must be after receiving the challenge ciphertext
$\;\;\;\;$ and
$\;$ after submitting ciphertext(s), the adversary also can't submit any plaintexts

.