This route is at least 0.8 seconds (48 frames) faster than the one used in the currently published run. I do not plan on improving that TAS; this is merely a demonstration proving that taking the bonus round path is indeed faster than the standard route. This is also not super optimized for finer movements or reducing lag, so the time save could be even greater.
HP was set to 1 from the cheats menu for ease of setup, which you must have by the bonus round to lose it as fast as possible. In a full-game TAS setting, this level is normally entered with 2 HP, but I imagine an additional one could be lost on Day 2: Metalhead for negligible time loss.