OCaml GET JSON through curl with a hard timeout

(* OCaml's stdlib has no HTTP client; shelling out to curl adds no dependencies. *)
let http_get_json ~url ~timeout ~key =
  let cmd = Printf.sprintf "curl -fsS --max-time %g %s" timeout (Filename.quote url) in
  let ic = Unix.open_process_in cmd in
  let body = In_channel.input_all ic in
  match Unix.close_process_in ic with
  | Unix.WEXITED 0 ->
    let q = String.make 1 '"' in
    let needle = q ^ key ^ q ^ ":" ^ q in
    let width = String.length needle in
    let rec seek i =
      if i + width > String.length body then Error (Printf.sprintf "missing JSON field %S" key)
      else if String.sub body i width = needle then
        match String.index_from_opt body (i + width) '"' with
        | Some stop -> Ok (String.sub body (i + width) (stop - i - width))
        | None -> Error (Printf.sprintf "unterminated value for %S" key)
      else seek (i + 1)
    in
    seek 0
  | _ -> Error (Printf.sprintf "GET %s failed or timed out" url)