Hello Jacob,
There is a problem with keywords field, which cannot be indexed.
It seems that it can be solved by adding this case in the first foreach : 

elseif ($field_name == 'biblio_keywords') {
$callback_item_type = 'setter callback';
$callback_item_value = 'entity_property_verbatim_set';
$field_data_type = 'list<text>';
}

If you think it's correct, could you add it to the biblio_search_api.module ?
Many thanks.
Stéphanie