Wow! I don't envy you that at all.
As you say the buck was "very much alive" and that the head was not visible, I personally would not be wanting to use a knife with the public gathered round.
So perhaps moderated .410 with sub-sonic loads, aimed at the spine (as close to neck as possible), and with the barrel angled down to avoid excess damage to the engine/car?
A concern would be where any spent shot might end up, which would influence the position from which to take the shot, but TBH when used on roe I've never found much of an exit wound.