Hi there Buck,
Are you talking about a mooring or anchorage? The reasons for swing can have to do with how you're attached to the mooring ball--this is why I ask.
Onwards, assuming anchoring or attached to a mooring anchor NOT the mooring ball, things should be the same...
Yawls and Ketches are known to leave the mizzen sail up as a riding sail to keep the boat from hunting about while at anchor. I've never seen the type of sail you're talking about. However, your topping lift holds your boom up while not underway since I don't believe your boat would have a boom gallows or boom crutch. I wouldn't want to use my topping lift for the purpose you describe.
I do not speak with authority on the subject but it would seem that the backstay would be the place that one would place a riding sail--and rig it to one side or the other of the boat. Depending on the reason your boat is sailing about on anchor, you may have other things you could do--I've heard of folks hanging a bucket or drogue from the anchor chain just below the surface of the water to achieve the same results w/o a riding sail; also you may be able to use a bridle and adjust your boat's angle to wind and waves to achieve less hunting about.
Finally, if you are at a mooring and you're attached to the ball rather than to a line that goes down to the mooring anchor/block (whatever it is secured to) then that could be part of the problem. If all the other boats are attached in the same manner, though, it would seem strange that only your boat is having problems.
Best of luck to you