First, don't go backwards if you are using any friction stand alone sway bar. They potential to bend and break when backing and especially when turning and backing. (you didn't say how you broke yours). And yes, if you have to go backwards, you have to get out of the tow vehicle, walk to the hitch, and un-connect the sway bar. Then when you are ready to drive forward again, you put it back on.
Second, tighten it down as much as you can. Put all your weight into the final "umph". Then back it off about 1/4 turn. They are suppose to be tight. The greater the friction, the more effective they are.
There is always a little slop where the bar attaches to both little balls.
If you are already doing this, then, as stated above, something else is causing the sway.
The most common problem for sway is loading the rear of the trailer too heavy, making the tongue light. Even with the best of hitches and sway control, a tail-heavy trailer will sway ... horribly.
If you are loaded correct with good tongue weight, the suspension on your tow vehicle may not be stout enough.
Another problem may be the tow vehicle is just too short for the length of trailer you are towing (wheel base).
Worn rear shocks on the tow vehicle is also a potential for agitating trailer sway.
If your weight distribution is not set right, you may experience unwanted sway. Front wheels too light can cause steering issues that will induce trailer sway. Rear of tow vehicle too light also and weird things can happen.
First, you can't fix an inferior tow vehicle. If the tow vehicle is just not adequate for the trailer being pulled, no matter how you try to patch it, it won't fix the problem.
Second, an inferior friction sway bar will work pretty much the same as an expensive top name brand one will. The only difference is, the inferior one may someday fail, fall apart, or breaks where the better made one would not.
Third, consider a weight distribution system that already has sway control built in. For example Reese Dual Cam or the Equal-i-zer type systems. Then backing is not an issue at all.
To spend thousands of dollars on a tow vehicle, and then to spend thousands of dollars on a trailer, and then load your most precious cargo (your family) all riding on a mediocre hitch system is just nuts!
Remember the tire commercial on television with the baby sitting inside the automobile tire. And then the statement is made, Michelin - Because so much is riding on your tires. .... same is true for your hitch.