Hi there,
After taking the GRE 4 times, you probably have a good sense for how much upside you have left in your score. If you think there's still some room to budge, then I would encourage you to try for it. (You want to put your best foot forward, right?!) Although Columbia doesn't report GRE scores, we know what the average is at a few similar programs (namely 164V/162Q at Yale SOM) - so getting your quant score closer to that average could help you be more competitive. With that said, it's only one data point in a holistic application and it sounds like you have a pretty compelling background/story that will help offset some softer stats. Since you've already taken some additional coursework, I'm not sure if adding another course will necessarily be the best use of your time, to be honest. The HBX CORe program is quite rigorous and highly quantitatively oriented so I think you covered most of your bases with that. But of course, taking another class definitely can't hurt.
I know that answer wasn't quite black & white but unfortunately neither is this decision
But I say go for the GRE re-take if you think there's a good chance of further improvement. Otherwise, you can take another course if you'd like, or shift your focus to the rest of the application. For Columbia, you'll have your best shot by taking advantage of rolling admissions and the early decision option (if it's your top choice school) - so apply early if you can!
Best of luck!
Kindly,
Melody