Here is my spin on the question.
The Taylor boys are pretty well versed in being able to feel where they have hooked the fish initially. This gives them the confidence to lean on the fish through out the whole fight.
I also believe the action of their rods might make it look like they are resetting hooks, but in fact I believe they are just "yanking" or aggressively "pumping and winding". In other words they are using a COME HERE technique.
I believe it works very effectively as how many times did the Taylor’s have green fish either charge towards the boat or have issues with green fish taking them around or under the boat?
Effectively they are ensuring that the barra swim towards them without letting them run to far away and have to chase them.
I believe this technique is very similar to deep water jigging techniques that most people use. Look at the action of a parabolic rod when jigging and fighting hooked fish. When I have hooked fish in 100m+ you need to keep that pump and wind action going all the way to the boat to keep the fishes head pointed towards you but the rod looks like you are re-setting the hook time and time again.
Now their might be many reasons for this as JM has already alluded to. Not to spook feeding fish, not wanting to have a rampaging barra upsetting the current fish holding near that certain area or one thing that has been overlooked is lighter leaders.
When a barra runs away from you your leader in almost always being scuffed by their mouth and the pressure that is put on that line is the reason the barra wear through the leaders. Now imagine the opposite. A barra being pulled head first towards the boat by the scruff of its neck. I believe less wear and tear on the leader which could mean lighter leaders thus making your lures look different to everyone else’s and the actions will be much different.
By the way these are just my views on it and probably no where near the ballpark, but maybe food for thought?
Cheers
Lee