How to improve responsiveness of git hash in zsh prompt?

I wanted to put the current git hash in my prompt; but my initial approach was kind of laggy:

psvar="$(git log -n1 --pretty='format: %h' 2>/dev/null)"

(with $PROMPT including %1v to make that visible) I tried the vcs_info plugin, but that was also laggy. So I've ended up writing my own function:

function githead() {
  local commondir ref hash _
  local gitdir="${1:a}"
  until [[ -e "$gitdir/.git" ]]; do
    local updir="${gitdir%/*}"
    [[ "$updir" == "$gitdir" ]] && return 1
    gitdir="$updir"
  done
  gitdir="$gitdir/.git"
  [[ -f "$gitdir" ]] && read _ gitdir < "$gitdir"
  read _ ref < "$gitdir/HEAD"
  local commondir="$gitdir/commondir"
  [[ -e "$commondir" ]] && gitdir="$gitdir/$(<$commondir)"
  ref="$gitdir/$ref"
  read hash <"$ref"
  print -r "${hash::12}"
  return 0
}

It's certainly faster, but that's _bound_ to be brittle. In particular, a couple of the files I have to read look like they _could_ contain more than one line of content, and not necessarily put the line I want at the top. Is there a fast way of getting the current hash from git, which is more robust than what I've written by hand?