Insert custom taxonomy value

I've created a form for submitting content to a custom post type. The function below uses the gform_post_data hook to insert the submission and everything works great.

My problem: I'd like the user to also specify a custom taxonomy term. It's a hierarchical taxonomy structure, like categories.

I've hacked the Gravity Forms core (yes, I realize this is a bad idea) to display the appropriate category names in the category select list. Unfortunately, those values aren't being recorded.

What am I missing? Is there another line I need to add to specify the custom taxonomy name?

function omw_update_post_type($post_data, $form){
if($form["id"] == '1'){
$post_data["post_type"] = "rfp";
}
return $post_data;
}

add_filter("gform_post_data", "omw_update_post_type", 10, 2);