Golf clap!

And let's not forget the flight engineer on this crew.

Or the AC, who was medically grounded for 9 months but still flying operational missions.

QFT

This one said he was described as "polite", "quiet" and a "perfectionist" who "rarely drank and never smoked." One of his instructors remarked that his shoes were always shined.
Now that's more 'lifestyle.'  Certainly not one the military who frown on.

Thanks for the info, but I'm still not seeing anything that would indicate what 'lifestyle' mean in the context of being a contributing factor to an aircraft mishap.

I must be over thinking it.  The problem with that idea is that the military doesn't just pull words out its ass.

What if pilot PIC had lowered the nose, flew wings level and maintained flying speed AND did nothing else, what would the outcome be?

For a comparison look at this C-130 crash from 1992.   It was incorrect rudder input on this one.   Also simulated eng out.    That IP used to fly in my unit.

https://www.upi.com/Archives/1992/04/13/Cockpit-recorder-pinpoints-error-in-crash/4087703137600/

Not sure what you're looking for, here. It is for anything in the pilot's life outside of the cockpit that might have been a contributing factor to the accident. You can sift through all the AIB reports online if you so desire to see some of the specific items that the board looks at and would report on in that section.

In the one on the F-22 where the pilot retracted the gear early and the jet settled back on its belly, in that section it says,

Someone should have addressed your question by now... The answer is maybe

I have ZERO experience in a C130 or any Large multi engine but here are some of the circumstances that could make even that scenario problematic.

First this crew seemed to never grasp the seriousness of their situation or if they did made every possible wrong decision. I will make a guess but it is unlikely the extra time would have changed their decisions.

Any 4 engine has two different VMC speeds. VMC is the minimum controllable airspeed, with one or even two engines out. At VMC the aircraft can be controlled to fly straight ahead or within 20° with 150 lbs of rudder (max) input and a max bank angle of 5° 'away' from the dead engine(s). Doesn't mean climb it is only a controllable condition. At this point the dead engine(s) need to be cleaned up (feathered) and any other requirements like partial flaps, gear up, cowl flaps closed, etc. met. If this speed and conditions are not met, the aircraft will start an uncontrolled roll into the dead engine side. Many will think you can just add aileron against it but all you are doing is increasing the stall speed. If you are below VMC, the only solution is to trade altitude for for speed and you will have to reduce power on the good engines or you will not recover.

In smaller twins and not really in this particular accident, improper action can also slow you into the magic Region of Reverse Command. That is the speed where drag is so great you don't have enough power to accelerate. Again lowering he nose is the only solution there. The 'reverse' part comes from the fact that if you have power and increase it, the aircraft will actually slow more if you try to maintain altitude. Likewise reducing power and reducing angle of attack will increase speed.

When all this is taking place low to the ground it is very hard to push forward and see the ground rushing up! And in this case it would have been an overwhelming sight!

With their light loading and even with their high drag, it seems to me that if they went to level attitude, zero side slip, and 5° bank, it would have accelerated. Would that have changed the outcome in this case? Maybe

I hope that give you some idea of the complexity of the conditions that defy simple solutions.

The pilot should have stopped the aircraft when they noticed the engine issues well below V1.  End of story.

If he continued the takeoff, the situation was 100% survivable with the skills and techniques that are hammered into multi-engine pilots throughout their initial and follow on training.  I'm not a C-130 pilot but I've got lots of hours in Lockheed products and have been flying in the USAF for 18 years but this is fairly basic.

From other reports there were other issues the AIB did not discuss that contributed as well.  They should have never been flying that day.