MAybe I missed something...
... but no one seemed to give the BG credit for being able to simply redeploy his weapon from the Hostage's head 90° to shoot the hero while the hero is doing his lightning 2 second drill. Since firing is a fraction of a second and redeploying the weapon is as well, we seem to have a serious timeline gap here.
Action beats reaction, you can cover 3-5 yards faster than they can comprehend what you are doing, and react to your actions.
Maybe someone younger and faster than I can do that. As a lineman in that classic American youth ritual of high school football, I was very fast off of the line. Trouble was, a lot of people I rushed did comprehend what I did. Take the example further to pro or high level college football. Check the time it takes a rushing DT / DE to go 7 and 15 yards. They do that for a living and I don'T think any of us, even you young and well conditioned atheletes out there, can take out a BG in a 2 second drill from just standing there. Even at 7 yards would, it would be a good feat - remembering that you are trying to run, draw and whack this guy upside of the noggin.
If we were talking about charging a person without a hostage and using a knife, then you would be more realistic. I have drilled to defend against that and the only way I can save myself is by retreating and drawing.
I think that the risk of getting shot yourself is too great. You have such a low probability of success, really, so why not get some distance, maybe partial cover. Move to the opposite side of BG's gun to gain an advantage and try and get a deception game going (like, maybe tossing him your dummy wallet w/ ballistic shield
). Seriously, you are armed and BG doesn't know that until then. Unless the hostage is someone you have worked out a plan with and practiced in advance (e.g., husband/wife training), your best bet may be to ensure that you survive in order to help the hostage. When you have ensured a better chance of survival, like getting at least 15 yards away and maybe some cover - anything, a street sign post or telephone pole helps - then you can make your draw and hinder BG's plan to kill and escape or take the hostage and get away. I would let BG get away without the hostage rather than risk any life.