Watch Rob Leatham shoot this short course:
Note that he didn’t wait for the swingers, nor did he chase them. He shot them at their transition point, and at that point shooting them is pretty much like shooting a still target.
His sequence was this:
Shoot the back plate, then the activating poppers, then back to the first swinger just in time for it to reach its lull point, then to the other swinger at its lull point and finally the final plate.
Most course designers will give you other things to shoot while waiting for a swinger to hit the turn around point (where it is largely still). How much you bite off is up to your risk reward calculation.
You should know how long it will take a timer from activation to lull point. Then you can sort out what else you will shoot before aiming at the lull point to shoot it when it is moving the least.