To me, it's less about the rod "length" than it is the "action". I prefer a fast or very fast action tip rod over a slow to moderate action tip rod. It just seems to actually "shoot" the jig, rather than "sling/catapult" it.
That being said ... I did start out with a 5' & 5'6" UL and they did work OK. But when I broke my 5'6" and started using my 6'6" fast action rod ... I found out I could shoot the jig farther, plus I didn't have to use my arm as much when setting the hook.
I'm not aware of any "conditions" that warrant a specific length of rod, unless you're actually IN the boat slip of the dock and there's limited room for an upward hookset. As long as you're shooting from outside of the dock, the length of rod only dictates how close you can get to it.
I used 4# test mono (Stren Gold) for most of the first 10yrs of my dock shooting experience, and it did fine. In the last few years, I've gone to 6# copoly (Vicious Panfish) on my casting rods ... and since I now use those casting rods to shoot docks, I'm staying with 6# test. The rods have larger reels, and therefore larger reel spools, which translates to longer casts and less memory coils in the line.
I "have" used braid (PowerPro 10/2) to shoot docks, but not as my primary choice. I've also used rods from 5' - 8' in length, to shoot docks, but found a 6' to 6'6" rod to be the best choice (for me) ... as long as it had the fast action tip.
The biggest difference in using rods of different lengths ... is the timing of the line release. Shorter rod = quicker release (but only in tenths of a second). Practice (with whatever rod you choose) will show you the optimum release timing. I always tell people to wait until the jig passes the rod tip before releasing the line from the reel. That takes a bit of practice to get confident with. Release too soon = jig falls short .... release too late = jig flies too high ... release at the same time = jig goes nowhere.