The second verb should not be hissed, but hiss. However, you don’t use either the present or the past tense there. Rather, you use the bare infinitive, because that’s what do takes.
You can see that because you cannot use a tensed form of be when constructing the second part. That is, it would be
She’d didn’t so much have an inspiration as be an inspiration.
She’d didn’t so much have an inspiration as *was an inspiration.
It’s because the do auxiliary is outside the “so much X as Y” construct. When the entire first verb fills the X slot, and that is a tensed verb, you can do the same with the Y slot:
It wasn’t so much that she had an inspiration as that she was one.
or with do in both pieces, because it is inside and not factored out:
It wasn’t so much that she did call him as that she didn’t call him.
But now factoring it out in front of so much as:
She didn’t so much as answer him as not answer him.