I practically write a novel on the subject and you only disagree with one thing?
I don’t believe you. There must be more. Fess up!
But on that subject, the sequence of events that I envision is as follows:
A fleet is spawned and begins moving to target. As is typical, they form a line with some spaces between ships; neither a dense cluster nor a particularly spaced out line. Just far enough that they don’t have overlapping arcs of fire with each other. It is into that gap that the Independent Broadside or Hybrid Broadside embeds itself: drop out of warp and maneuver between those ships, situating within one ship’s firing arc, but directly astern another foe. The broadside then lets loose with port and starboard guns with the weapons officer switching back and forth between targets. It takes less than a second to reposition the cursor from one ship to the other unless there is a fair amount of lag. With a normal cycle time of 6 seconds and running at 300% power, the weapons officer would have a 2 second window to switch targets from A to B and back to A again without losing any dps in the process (except for what is sacrificed by not using manual beams).
I imagine the targets would die before other (non-fighter) enemies would close-in, since full damage is brought to bear on both targets. In this time, the ship is taking damage only from one enemy, and after they’re dead the independent / hybrid broadside goes looking for another such juicy gap, or is free to engage ‘normally’ with only one side. Overlapping Broadside wouldn’t have this capability.
But maybe opportunities like this aren’t as common as they subjectively seem.