You didn't get a structural engineer to design this, DID YOU? this structure was doomed to sway from inception.
You don't give limits, can you cross brace between the verticals, that would be easiest and most effective, it could improve the design parameters for the verticals as well but the calculation should be performed by someone who knows what she is doing. To make it a rigid frame would increase the demand for an experienced structural engineer.
Michael.
Timing has a lot to do with the outcome of a rain dance.