Unfortunately, I don't think this question is answerable, at least not with a definitive answer, because the answer is that it is undefined.
In the linked video, we're clearly looking at an aircraft that is being operated well outside of its design limits (overweight, out of balance, possibly high density altitude). Talking about which of the V_sub numbers is best to fly in this case is absurd, because all of those numbers assume the aircraft is being operated within its design performance envelope.
I have attached a basic L/D chart below. Notice how the lines behave toward the edges. A plane being operated outside of the envelope will be off the left side of this chart, where the numbers increase asymptotically. What this is saying is that there is eventually a configuration where the plane is incapable of flying at ANY number. I think the plane in the video was perilously close to that threshold.
As a glider pilot, we have the idea of "best speed to fly," which may be minimum sink, maximum glide (L/D), or any speed in the operating envelope of the aircraft. Min sink is usually just above stall speed, but you're moving pretty slow. It's ideal for climbing in a thermal, where you want to move slow. However, if you're doing a glider race, you'll want ballast in the wings for extra boost to the optimal l/d speed, so you can travel farther at a faster speed.
If you're in an area of sinking air, you'll go faster than best L/D. Flaps add drag. We only want to extend flaps when we're looking to decrease stall speed and fly slowly, at the expense of needing additional power to fly at that low speed. But, the only guidance for an overloaded plane is to remove weight before trying to take off.
