What's your request size and how big are the documents you're needing to parse? Even if you're returning 1000 documents, if you're not fetching the source as part of the request (do you need to?) or if you don't have a ton of fields, it shouldn't be too expensive to parse that to get the total number of hits.
I'm assuming he needs the source, otherwise he should look at the count API.
The count API just returns counts. I'm assuming he needs some fields to display which should be smaller than source if source is "large." Unfortunately we are left to guess at his statements because not enough detail is provided.